Associate Professor Holger Dullin

F07 - Carslaw Building
The University of Sydney

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

Selected grants

2011

  • Geometry and Analysis of Discrete Integrable Systems; Dullin H, Joshi N; Australian Research Council (ARC)/Discovery Projects (DP).

2010

  • Bodies in Space; Dullin H, O'Meara D, Graham K, 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

  • 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.
  • 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.
  • 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.
  • Dullin, H., Meiss, J. (2009). Quadratic volume-preserving maps: Invariant Circles and Bifurcations. SIAM Journal on Applied Dynamical Systems, 8(1), 76-128.
  • 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.
  • 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.
  • 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.
  • Davison, C., Dullin, H. (2007). Geodesic flow on three dimensional ellipsoids with equal semi-axes. Regular and Chaotic Dynamics, 12(2), 172-197.
  • 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.
  • 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.
  • 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.
  • Dullin, H., Meiss, J., Sterling, D. (2005). Symbolic codes for rotational orbits. SIAM Journal on Applied Dynamical Systems, 4(3), 515-562.
  • 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.
  • 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.
  • 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.
  • Dullin, H., Giacobbe, A., Cushman, R. (2004). Monodromy in the resonant swing spring. Physica D: Nonlinear Phenomena, 190(1-2), 15-37.
  • Dullin, H., Gottwald, G., Holm, D. (2004). On Asymptotically Equivalent Shallow Water Wave Equations. Physica D: Nonlinear Phenomena, 190(1-2), 1-14.
  • Dullin, H. (2004). Poisson integrator for symmetric rigid bodies. Regular and Chaotic Dynamics, 9(3), 255-264.
  • Waalkens, H., Dullin, H., Richter, P. (2004). The problem of two fixed centers: bifurcations, actions, monodromy. Physica D: Nonlinear Phenomena, 196, 265-310.
  • 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.
  • 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.
  • Dullin, H., Meiss, J. (2003). Twist singularities for symplectic maps. Chaos: an interdisciplinary journal of nonlinear science, 13(1), 1-16.
  • 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.

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]
  • 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.
  • 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.
  • 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.
  • Dullin, H., Meiss, J. (2009). Quadratic volume-preserving maps: Invariant Circles and Bifurcations. SIAM Journal on Applied Dynamical Systems, 8(1), 76-128.

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.
  • 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.
  • 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.
  • Davison, C., Dullin, H. (2007). Geodesic flow on three dimensional ellipsoids with equal semi-axes. Regular and Chaotic Dynamics, 12(2), 172-197.
  • 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.
  • 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.
  • 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.
  • Dullin, H., Meiss, J., Sterling, D. (2005). Symbolic codes for rotational orbits. SIAM Journal on Applied Dynamical Systems, 4(3), 515-562.
  • 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.

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.
  • 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.
  • Dullin, H., Giacobbe, A., Cushman, R. (2004). Monodromy in the resonant swing spring. Physica D: Nonlinear Phenomena, 190(1-2), 15-37.
  • Dullin, H., Gottwald, G., Holm, D. (2004). On Asymptotically Equivalent Shallow Water Wave Equations. Physica D: Nonlinear Phenomena, 190(1-2), 1-14.
  • Dullin, H. (2004). Poisson integrator for symmetric rigid bodies. Regular and Chaotic Dynamics, 9(3), 255-264.
  • Waalkens, H., Dullin, H., Richter, P. (2004). The problem of two fixed centers: bifurcations, actions, monodromy. Physica D: Nonlinear Phenomena, 196, 265-310.

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.
  • 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.
  • Dullin, H., Meiss, J. (2003). Twist singularities for symplectic maps. Chaos: an interdisciplinary journal of nonlinear science, 13(1), 1-16.

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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