Professor Holger Dullin

Telephone 9351 4083
Fax 9351 4534

Website maths homepage

Research interests

Dynamical systems with special emphasis on Hamiltonian systems; rigid body dynamics with applications in biomechanics; topology of integrable systems, especially (quantum) monodromy; semiclassical quantization; volume preserving mappings.

Member of the Applied Mathematics Research Group.

Teaching and supervision

Timetable

HR_Dullin

Current research students

Project title Research student
Doubly Transient Chaos in Celestial Mechanics Lachlan BURTON
Relating Classical and Quantum Integrable Systems Sean DAWSON
Classification of integrable systems arising from separation of variables Diana NGUYEN

Selected grants

2015

  • Analysing the movement characteristics of Thai dance; Fong Yan A, Smith R, Dullin H; University of Sydney/Sydney Southeast Asia Centre.

2011

  • Geometry and Analysis of Discrete Integrable Systems; Dullin H, Joshi N; Australian Research Council (ARC)/Discovery Projects (DP).
  • Bodies in Space; Dullin H, O'Meara D, Sinclair P, Singh S, O'Meara D; Australian Research Council (ARC)/Linkage Projects (LP).

2007

  • LMS Collab. Grant: East Midlands Mathematical Physics Seminar; Dullin H; London Mathematical Society/Research Support.

2006

  • British Council Collaboration Grant; Dullin H, Tsygvintsev A; The British Council/Research Support.

Selected publications

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Journals

  • Chiscop, I., Dullin, H., Efstathiou, K., Waalkens, H. (2019). A Lagrangian fibration of the isotropic 3-dimensional harmonic oscillator with monodromy. Journal of Mathematical Physics, 60(3), 032103-1-032103-15. [More Information]
  • Martynchuk, N., Dullin, H., Efstathiou, K., Waalkens, H. (2019). Scattering invariants in Euler�s two-center problem. Nonlinearity, 32(4), 1296-1326. [More Information]
  • Alonso, J., Dullin, H., Hohloch, S. (2019). Taylor series and twisting-index invariants of coupled spin�oscillators. Journal of Geometry and Physics, 140(June 2019), 131-151. [More Information]
  • Tong, W., Dullin, H. (2019). Using the geometric phase to optimize planar somersaults. IMA Journal of Applied Mathematics, 84(13 April 2019), 44-62. [More Information]
  • Dullin, H., Waalkens, H. (2018). Defect in the Joint Spectrum of Hydrogen due to Monodromy. Physical Review Letters, 120(2), 1-5. [More Information]
  • Dullin, H., Worthington, J. (2018). Stability Results for Idealized Shear Flows on a Rectangular Periodic Domain. Journal of Mathematical Fluid Mechanics, 20(2), 473-484. [More Information]
  • Dullin, H. (2017). A New Twisting Somersault. SIAM News, 50(2), 12 pages.
  • Tong, W., Dullin, H. (2017). A new twisting somersault: 513XD. Journal of Nonlinear Science, 27, 2037-2061. [More Information]
  • Dullin, H., Pelayo, A. (2016). Generating Hyperbolic Singularities in Semitoric Systems Via Hopf Bifurcations. Journal of Nonlinear Science, 26(3), 787-811. [More Information]
  • Dullin, H., Marangell, R., Worthington, J. (2016). Instability of equilibria for the two-dimensional euler equations on the torus. SIAM Journal on Applied Mathematics, 76(4), 1446-1470. [More Information]
  • Dullin, H., Montgomery, R. (2016). Syzygies in the two center problem. Nonlinearity, 29(4), 1212-1237. [More Information]
  • Bharadwaj, S., Duignan, N., Dullin, H., Leung, K., Tong, W. (2016). The diver with a rotor. Indagationes Mathematicae, 27(5), 1147-1161. [More Information]
  • Dullin, H., Tong, W. (2016). Twisting Somersault. SIAM Journal on Applied Dynamical Systems, 15(4), 1806-1822. [More Information]
  • Arunasalam, S., Dullin, H., Nguyen, M. (2015). The Lie-Poisson structure of the symmetry reduced regularized n-body problem. Journal of Physics A: Mathematical and Theoretical, 48(6), 1-12. [More Information]
  • Dullin, H., Worthington, J. (2014). The vanishing twist in the restricted three-body problem. Physica D: Nonlinear Phenomena, 276, 12-20. [More Information]
  • Rose, D., Dullin, H. (2013). A symplectic integrator for the symmetry reduced and regularised planar 3-body problem with vanishing angular momentum. Celestial Mechanics and Dynamical Astronomy, 117(2), 169-185. [More Information]
  • Papadopoulos, G., Dullin, H. (2013). Semi-global symplectic invariants of the euler top. Journal of Geometric Mechanics, 5(2), 215-232. [More Information]
  • Dullin, H. (2013). Semi-global symplectic invariants of the spherical pendulum. Journal of Differential Equations, 254(7), 2942-2963. [More Information]
  • Dullin, H. (2013). The Lie-Poisson structure of the reduced n-body problem. Nonlinearity, 26(6), 1565-1579. [More Information]
  • Dullin, H., Meiss, J. (2012). Resonances and Twist in Volume-Preserving Mappings. SIAM Journal on Applied Dynamical Systems, 11(1), 319-349. [More Information]
  • Dullin, H., Lomeli, H., Meiss, J. (2012). Symmetry reduction by lifting for maps. Nonlinearity, 25(6), 1709-1733. [More Information]
  • Dullin, H., Hanssmann, H. (2012). The degenerate C. Neumann system I: Symmetry reduction and convexity. Central European Journal of Mathematics, 10(5), 1627-1654. [More Information]
  • Tong, W., Dullin, H. (2012). The Equilateral Pentagon at Zero Angular Momentum: Maximal Rotation through Optimal Deformation. SIAM Journal on Applied Dynamical Systems, 11(3), 963-987. [More Information]
  • Schmidt, S., Dullin, H. (2010). Dynamics near the p:-q resonance. Physica D: Nonlinear Phenomena, 239(19), 1884-1891. [More Information]
  • Schmidt, S., Dullin, H., Richter, P. (2009). A Poincare section for the general heavy rigid body. SIAM Journal on Applied Dynamical Systems, 8(1), 371-389. [More Information]
  • Dullin, H., Waalkens, H. (2009). Dullin and Waalkens Reply {to comment on "Non-uniqueness of the phase shift in central scattering due to monodromy"}. Physical Review Letters, 102(18), 188902-1-188902-1. [More Information]
  • Fitch, N., Weidner, C., Parazzoli, L., Dullin, H., Lewandowski, H. (2009). Experimental demonstration of classical Hamiltonian monodromy in the 1:1:2 resonant elastic pendulum. Physical Review Letters, 103(3), 034301-1-034301-4. [More Information]
  • Dullin, H., Meiss, J. (2009). Quadratic volume-preserving maps: Invariant Circles and Bifurcations. SIAM Journal on Applied Dynamical Systems, 8(1), 76-128. [More Information]
  • Dullin, H., Meiss, J. (2008). Nilpotent normal form for divergence-free vector fields and volume-preserving maps. Physica D: Nonlinear Phenomena, 237(2), 156-166. [More Information]
  • Dullin, H., Waalkens, H. (2008). Nonuniqueness of the phase shift in central scattering due to monodromy. Physical Review Letters, 101(7), 070405-1-070405-4. [More Information]
  • Dullin, H., Tsygvintsev, A. (2008). On the analytic non-integrability of the rattleback problem. Universite Paul Sabatier. Faculte des Sciences. Annales: mathematiques, 17(3), 495-517.
  • Dullin, H., Schmidt, S., Richter, P., Grossmann, S. (2007). Extended phase diagram of the Lorenz model. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 17(9), 3013-3033. [More Information]
  • Davison, C., Dullin, H. (2007). Geodesic flow on three dimensional ellipsoids with equal semi-axes. Regular and Chaotic Dynamics, 12(2), 172-197. [More Information]
  • Davison, C., Dullin, H., Bolsinov, A. (2007). Geodesics on the ellipsoid and monodromy. Journal of Geometry and Physics, 57(12), 2437-2454. [More Information]
  • Dullin, H., Tsygvintsev, A. (2007). On the analytic non-integrability of the rattleback problem. Universite Paul Sabatier. Faculte des Sciences. Annales: mathematiques.
  • Dullin, H., Ngoc, S. (2007). Symplectic Invariants Near Hyperbolic-Hyperbolic Points. Regular and Chaotic Dynamics, 12(6), 689-716.
  • Cushman, R., Dullin, H., Hanssmann, H., Schmidt, S. (2007). The 1:±2 resonance. Regular and Chaotic Dynamics, 12(6), 642-663.
  • Dullin, H., Ivanov, A., Meiss, J. (2006). Normal forms for 4D symplectic maps with twist singularities. Physica D: Nonlinear Phenomena, 215(2), 175-190. [More Information]
  • Bolsinov, A., Dullin, H., Veselov, A. (2006). Spectra of Sol-Manifolds: Arithmetic and Quantum Monodromy. Communications in Mathematical Physics, 264(3), 583-611. [More Information]
  • Dullin, H., Ivanov, A. (2005). Another look at the saddle-centre bifurcation: Vanishing twist. Physica D: Nonlinear Phenomena, 211(1-2), 47-56. [More Information]
  • Dullin, H., Robbins, J., Waalkens, H., Creagh, S., Tanner, G. (2005). Maslov indices and monodromy. Journal of Physics A: Mathematical and General, 38(24), L443-L447. [More Information]
  • Dullin, H., Meiss, J., Sterling, D. (2005). Symbolic codes for rotational orbits. SIAM Journal on Applied Dynamical Systems, 4(3), 515-562. [More Information]
  • Dullin, H., Ivanov, A. (2005). Twistless tori near low order resonances. Journal of Mathematical Sciences, 128(2), 2754-2760. [More Information]
  • Dullin, H., Ivanov, A. (2005). Vanishing twist in the Hamiltonian Hopf bifurcation. Physica D: Nonlinear Phenomena, 201(1-2), 27-44. [More Information]
  • Dullin, H., Matveev, V. (2004). A new integrable system on the sphere. Mathematical Research Letters, 11(6), 715-722.
  • Dullin, H., Fasso, F. (2004). An algorithm for detecting directional quasi-convexity. Bit (Lisse): numerical mathematics, 44, 571-584. [More Information]
  • Cushman, R., Dullin, H., Giacobbe, A., Holm, D., Joyeux, M., Lynch, P., Sadovskii, D., Zhilinskii, B. (2004). CO2 molecule as a quantum realization of the 1:1:2 resonant swing-spring with monodromy. Physical Review Letters, 93(2), 024302-1-024302-4. [More Information]
  • Dullin, H., Giacobbe, A., Cushman, R. (2004). Monodromy in the resonant swing spring. Physica D: Nonlinear Phenomena, 190(1-2), 15-37. [More Information]
  • Dullin, H., Gottwald, G., Holm, D. (2004). On Asymptotically Equivalent Shallow Water Wave Equations. Physica D: Nonlinear Phenomena, 190(1-2), 1-14. [More Information]
  • Dullin, H. (2004). Poisson integrator for symmetric rigid bodies. Regular and Chaotic Dynamics, 9(3), 255-264. [More Information]
  • Waalkens, H., Dullin, H., Richter, P. (2004). The problem of two fixed centers: bifurcations, actions, monodromy. Physica D: Nonlinear Phenomena, 196, 265-310. [More Information]
  • Dullin, H., Gottwald, G., Holm, D. (2003). Camassa-Holm, Korteweg-de Vries-5 and other asymptotically equivalent equations for shallow water waves. Fluid Dynamics Research, 33(1), 73-95. [More Information]
  • Waalkens, H., Junge, A., Dullin, H. (2003). Quantum monodromy in the two-centre problem. Journal of Physics A: Mathematical and General, 36(20), L307-L314. [More Information]
  • Dullin, H., Meiss, J. (2003). Twist singularities for symplectic maps. Chaos, 13(1), 1-16. [More Information]
  • Dullin, H., Horányi, M., Howard, J. (2002). Generalizations of the Störmer problem for dust grain orbits. Physica D: Nonlinear Phenomena, 171(3), 178-195.
  • Waalkens, H., Dullin, H. (2002). Quantum monodromy in prolate ellipsoidal billiards. Annals of Physics, 295(1), 81-112. [More Information]
  • Dullin, H., Backer, A. (2001). About ergodicity in the family of Lima¸con billiards. Nonlinearity.
  • Dullin, H., Richter, P., Veselov, A., Waalkens, H. (2001). Actions of the Neumann system via Picard-Fuchs equations. Physica D: Nonlinear Phenomena, 155, 159-183.
  • Dullin, H., Gottwald, G., Holm, D. (2001). An Integrable Shallow Water Equation with Linear and Nonlinear Dispersion. Physical Review Letters, 87(19), 4501-4504.

Conferences

  • Dullin, H., Tong, W. (2013). Geometric phase in diving. Diving Research Worldwide : 1st Symposium for Researchers in Diving, Hamburg, Germany: Verlag.

2019

  • Chiscop, I., Dullin, H., Efstathiou, K., Waalkens, H. (2019). A Lagrangian fibration of the isotropic 3-dimensional harmonic oscillator with monodromy. Journal of Mathematical Physics, 60(3), 032103-1-032103-15. [More Information]
  • Martynchuk, N., Dullin, H., Efstathiou, K., Waalkens, H. (2019). Scattering invariants in Euler�s two-center problem. Nonlinearity, 32(4), 1296-1326. [More Information]
  • Alonso, J., Dullin, H., Hohloch, S. (2019). Taylor series and twisting-index invariants of coupled spin�oscillators. Journal of Geometry and Physics, 140(June 2019), 131-151. [More Information]
  • Tong, W., Dullin, H. (2019). Using the geometric phase to optimize planar somersaults. IMA Journal of Applied Mathematics, 84(13 April 2019), 44-62. [More Information]

2018

  • Dullin, H., Waalkens, H. (2018). Defect in the Joint Spectrum of Hydrogen due to Monodromy. Physical Review Letters, 120(2), 1-5. [More Information]
  • Dullin, H., Worthington, J. (2018). Stability Results for Idealized Shear Flows on a Rectangular Periodic Domain. Journal of Mathematical Fluid Mechanics, 20(2), 473-484. [More Information]

2017

  • Dullin, H. (2017). A New Twisting Somersault. SIAM News, 50(2), 12 pages.
  • Tong, W., Dullin, H. (2017). A new twisting somersault: 513XD. Journal of Nonlinear Science, 27, 2037-2061. [More Information]

2016

  • Dullin, H., Pelayo, A. (2016). Generating Hyperbolic Singularities in Semitoric Systems Via Hopf Bifurcations. Journal of Nonlinear Science, 26(3), 787-811. [More Information]
  • Dullin, H., Marangell, R., Worthington, J. (2016). Instability of equilibria for the two-dimensional euler equations on the torus. SIAM Journal on Applied Mathematics, 76(4), 1446-1470. [More Information]
  • Dullin, H., Montgomery, R. (2016). Syzygies in the two center problem. Nonlinearity, 29(4), 1212-1237. [More Information]
  • Bharadwaj, S., Duignan, N., Dullin, H., Leung, K., Tong, W. (2016). The diver with a rotor. Indagationes Mathematicae, 27(5), 1147-1161. [More Information]
  • Dullin, H., Tong, W. (2016). Twisting Somersault. SIAM Journal on Applied Dynamical Systems, 15(4), 1806-1822. [More Information]

2015

  • Arunasalam, S., Dullin, H., Nguyen, M. (2015). The Lie-Poisson structure of the symmetry reduced regularized n-body problem. Journal of Physics A: Mathematical and Theoretical, 48(6), 1-12. [More Information]

2014

  • Dullin, H., Worthington, J. (2014). The vanishing twist in the restricted three-body problem. Physica D: Nonlinear Phenomena, 276, 12-20. [More Information]

2013

  • Rose, D., Dullin, H. (2013). A symplectic integrator for the symmetry reduced and regularised planar 3-body problem with vanishing angular momentum. Celestial Mechanics and Dynamical Astronomy, 117(2), 169-185. [More Information]
  • Dullin, H., Tong, W. (2013). Geometric phase in diving. Diving Research Worldwide : 1st Symposium for Researchers in Diving, Hamburg, Germany: Verlag.
  • Papadopoulos, G., Dullin, H. (2013). Semi-global symplectic invariants of the euler top. Journal of Geometric Mechanics, 5(2), 215-232. [More Information]
  • Dullin, H. (2013). Semi-global symplectic invariants of the spherical pendulum. Journal of Differential Equations, 254(7), 2942-2963. [More Information]
  • Dullin, H. (2013). The Lie-Poisson structure of the reduced n-body problem. Nonlinearity, 26(6), 1565-1579. [More Information]

2012

  • Dullin, H., Meiss, J. (2012). Resonances and Twist in Volume-Preserving Mappings. SIAM Journal on Applied Dynamical Systems, 11(1), 319-349. [More Information]
  • Dullin, H., Lomeli, H., Meiss, J. (2012). Symmetry reduction by lifting for maps. Nonlinearity, 25(6), 1709-1733. [More Information]
  • Dullin, H., Hanssmann, H. (2012). The degenerate C. Neumann system I: Symmetry reduction and convexity. Central European Journal of Mathematics, 10(5), 1627-1654. [More Information]
  • Tong, W., Dullin, H. (2012). The Equilateral Pentagon at Zero Angular Momentum: Maximal Rotation through Optimal Deformation. SIAM Journal on Applied Dynamical Systems, 11(3), 963-987. [More Information]

2010

  • Schmidt, S., Dullin, H. (2010). Dynamics near the p:-q resonance. Physica D: Nonlinear Phenomena, 239(19), 1884-1891. [More Information]

2009

  • Schmidt, S., Dullin, H., Richter, P. (2009). A Poincare section for the general heavy rigid body. SIAM Journal on Applied Dynamical Systems, 8(1), 371-389. [More Information]
  • Dullin, H., Waalkens, H. (2009). Dullin and Waalkens Reply {to comment on "Non-uniqueness of the phase shift in central scattering due to monodromy"}. Physical Review Letters, 102(18), 188902-1-188902-1. [More Information]
  • Fitch, N., Weidner, C., Parazzoli, L., Dullin, H., Lewandowski, H. (2009). Experimental demonstration of classical Hamiltonian monodromy in the 1:1:2 resonant elastic pendulum. Physical Review Letters, 103(3), 034301-1-034301-4. [More Information]
  • Dullin, H., Meiss, J. (2009). Quadratic volume-preserving maps: Invariant Circles and Bifurcations. SIAM Journal on Applied Dynamical Systems, 8(1), 76-128. [More Information]

2008

  • Dullin, H., Meiss, J. (2008). Nilpotent normal form for divergence-free vector fields and volume-preserving maps. Physica D: Nonlinear Phenomena, 237(2), 156-166. [More Information]
  • Dullin, H., Waalkens, H. (2008). Nonuniqueness of the phase shift in central scattering due to monodromy. Physical Review Letters, 101(7), 070405-1-070405-4. [More Information]
  • Dullin, H., Tsygvintsev, A. (2008). On the analytic non-integrability of the rattleback problem. Universite Paul Sabatier. Faculte des Sciences. Annales: mathematiques, 17(3), 495-517.

2007

  • Dullin, H., Schmidt, S., Richter, P., Grossmann, S. (2007). Extended phase diagram of the Lorenz model. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 17(9), 3013-3033. [More Information]
  • Davison, C., Dullin, H. (2007). Geodesic flow on three dimensional ellipsoids with equal semi-axes. Regular and Chaotic Dynamics, 12(2), 172-197. [More Information]
  • Davison, C., Dullin, H., Bolsinov, A. (2007). Geodesics on the ellipsoid and monodromy. Journal of Geometry and Physics, 57(12), 2437-2454. [More Information]
  • Dullin, H., Tsygvintsev, A. (2007). On the analytic non-integrability of the rattleback problem. Universite Paul Sabatier. Faculte des Sciences. Annales: mathematiques.
  • Dullin, H., Ngoc, S. (2007). Symplectic Invariants Near Hyperbolic-Hyperbolic Points. Regular and Chaotic Dynamics, 12(6), 689-716.
  • Cushman, R., Dullin, H., Hanssmann, H., Schmidt, S. (2007). The 1:±2 resonance. Regular and Chaotic Dynamics, 12(6), 642-663.

2006

  • Dullin, H., Ivanov, A., Meiss, J. (2006). Normal forms for 4D symplectic maps with twist singularities. Physica D: Nonlinear Phenomena, 215(2), 175-190. [More Information]
  • Bolsinov, A., Dullin, H., Veselov, A. (2006). Spectra of Sol-Manifolds: Arithmetic and Quantum Monodromy. Communications in Mathematical Physics, 264(3), 583-611. [More Information]

2005

  • Dullin, H., Ivanov, A. (2005). Another look at the saddle-centre bifurcation: Vanishing twist. Physica D: Nonlinear Phenomena, 211(1-2), 47-56. [More Information]
  • Dullin, H., Robbins, J., Waalkens, H., Creagh, S., Tanner, G. (2005). Maslov indices and monodromy. Journal of Physics A: Mathematical and General, 38(24), L443-L447. [More Information]
  • Dullin, H., Meiss, J., Sterling, D. (2005). Symbolic codes for rotational orbits. SIAM Journal on Applied Dynamical Systems, 4(3), 515-562. [More Information]
  • Dullin, H., Ivanov, A. (2005). Twistless tori near low order resonances. Journal of Mathematical Sciences, 128(2), 2754-2760. [More Information]
  • Dullin, H., Ivanov, A. (2005). Vanishing twist in the Hamiltonian Hopf bifurcation. Physica D: Nonlinear Phenomena, 201(1-2), 27-44. [More Information]

2004

  • Dullin, H., Matveev, V. (2004). A new integrable system on the sphere. Mathematical Research Letters, 11(6), 715-722.
  • Dullin, H., Fasso, F. (2004). An algorithm for detecting directional quasi-convexity. Bit (Lisse): numerical mathematics, 44, 571-584. [More Information]
  • Cushman, R., Dullin, H., Giacobbe, A., Holm, D., Joyeux, M., Lynch, P., Sadovskii, D., Zhilinskii, B. (2004). CO2 molecule as a quantum realization of the 1:1:2 resonant swing-spring with monodromy. Physical Review Letters, 93(2), 024302-1-024302-4. [More Information]
  • Dullin, H., Giacobbe, A., Cushman, R. (2004). Monodromy in the resonant swing spring. Physica D: Nonlinear Phenomena, 190(1-2), 15-37. [More Information]
  • Dullin, H., Gottwald, G., Holm, D. (2004). On Asymptotically Equivalent Shallow Water Wave Equations. Physica D: Nonlinear Phenomena, 190(1-2), 1-14. [More Information]
  • Dullin, H. (2004). Poisson integrator for symmetric rigid bodies. Regular and Chaotic Dynamics, 9(3), 255-264. [More Information]
  • Waalkens, H., Dullin, H., Richter, P. (2004). The problem of two fixed centers: bifurcations, actions, monodromy. Physica D: Nonlinear Phenomena, 196, 265-310. [More Information]

2003

  • Dullin, H., Gottwald, G., Holm, D. (2003). Camassa-Holm, Korteweg-de Vries-5 and other asymptotically equivalent equations for shallow water waves. Fluid Dynamics Research, 33(1), 73-95. [More Information]
  • Waalkens, H., Junge, A., Dullin, H. (2003). Quantum monodromy in the two-centre problem. Journal of Physics A: Mathematical and General, 36(20), L307-L314. [More Information]
  • Dullin, H., Meiss, J. (2003). Twist singularities for symplectic maps. Chaos, 13(1), 1-16. [More Information]

2002

  • Dullin, H., Horányi, M., Howard, J. (2002). Generalizations of the Störmer problem for dust grain orbits. Physica D: Nonlinear Phenomena, 171(3), 178-195.
  • Waalkens, H., Dullin, H. (2002). Quantum monodromy in prolate ellipsoidal billiards. Annals of Physics, 295(1), 81-112. [More Information]

2001

  • Dullin, H., Backer, A. (2001). About ergodicity in the family of Lima¸con billiards. Nonlinearity.
  • Dullin, H., Richter, P., Veselov, A., Waalkens, H. (2001). Actions of the Neumann system via Picard-Fuchs equations. Physica D: Nonlinear Phenomena, 155, 159-183.
  • Dullin, H., Gottwald, G., Holm, D. (2001). An Integrable Shallow Water Equation with Linear and Nonlinear Dispersion. Physical Review Letters, 87(19), 4501-4504.

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