Associate Professor Milena Radnovic
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Associate Professor Milena Radnovic

Phone
9351 5782
Fax
9351 4534
Address
F07 - Carslaw Building
The University of Sydney
Associate Professor Milena Radnovic
PhD in Mathematics, 2003, University of Belgrade

My research interests are in Geometry of Integrable Dynamical Systems.

My research experience includes mathematical billiards, theory of algebraic curves, their Jacobians and theta- functions, ergodic theory, integrable systems on lattices and Yang-Baxter equations, singularity theory, Painlevé equations, topology of integrable systems.

Project titleResearch student
Billiard Dynamics in Projective Spaces Over Fields with Finite CharacteristicsHarry HIATT

Publications

Books

  • Dragovic, V., Radnovic, M. (2011). Poncelet Porisms and Beyond: Integrable Billiards, Hyperelliptic Jacobians and Pencils of Quadrics, Frontiers in Mathematics. Basel: Birkhauser (imprint of Springer).
  • Dragovic, V., Radnovic, M. (2010). Integrable Billiards, Quadrics, and Higher-dimensional Poncelet Porisms (in Russian). Moscow-Izhevsk: Regular & Chaotic Dynamics.

Book Chapters

  • Gasiorek, S., Radnovic, M. (2024). Periodic trajectories and topology of the integrable Boltzmann system. In Toshitake Kohno and Masanori Morishita (Eds.), Contemporary Mathematics, (pp. 111-130). Providence, Rhode Island: American Mathematical Society. [More Information]
  • Dragovic, V., Radnovic, M., Ranomenjanahary, R. (2020). Pencils of Quadrics, Billiard Double-Reflection and Confocal Incircular Nets. In Ron Donagi and Tony Shaska (Eds.), Integrable Systems and Algebraic Geometry, (pp. 133-166). Cambridge: Cambridge University Press. [More Information]
  • Dragovic, V., Radnovic, M. (2020). Periodic Trajectories of Ellipsoidal Billiards in the 3-Dimensional Minkowski Space. In Frank Nijhoff, Yang Shi, Da-Jun Zhang (Eds.), Asymptotic, Algebraic and Geometric Aspects of Integrable Systems, (pp. 159-174). Cham: Springer. [More Information]

Journals

  • Dragović, V., Radnovic, M. (2024). Isoperiodic families of Poncelet polygons inscribed in a circle and circumscribed about conics from a confocal pencil. Geometriae Dedicata, 218(3), Article no. 81 - 1-Article no. 81 - 23. [More Information]
  • Dragovic, V., Radnovic, M. (2023). Billiards within ellipsoids in the 4-dimensional pseudo-Euclidean spaces. Regular and Chaotic Dynamics, 28(1), 14-43. [More Information]
  • Andrews, G., Dragovic, V., Radnovic, M. (2023). Combinatorics of periodic ellipsoidal billiards. The Ramanujan Journal, 61, 135-147. [More Information]

2024

  • Dragović, V., Radnovic, M. (2024). Isoperiodic families of Poncelet polygons inscribed in a circle and circumscribed about conics from a confocal pencil. Geometriae Dedicata, 218(3), Article no. 81 - 1-Article no. 81 - 23. [More Information]
  • Gasiorek, S., Radnovic, M. (2024). Periodic trajectories and topology of the integrable Boltzmann system. In Toshitake Kohno and Masanori Morishita (Eds.), Contemporary Mathematics, (pp. 111-130). Providence, Rhode Island: American Mathematical Society. [More Information]

2023

  • Dragovic, V., Radnovic, M. (2023). Billiards within ellipsoids in the 4-dimensional pseudo-Euclidean spaces. Regular and Chaotic Dynamics, 28(1), 14-43. [More Information]
  • Andrews, G., Dragovic, V., Radnovic, M. (2023). Combinatorics of periodic ellipsoidal billiards. The Ramanujan Journal, 61, 135-147. [More Information]
  • Heu, V., Joshi, N., Radnovic, M. (2023). Global asymptotics of the sixth Painleve equation in Okamoto’s space. Forum of Mathematics, Sigma, 11, e17 - 1-e17 - 38. [More Information]

2022

  • Dragovic, V., Gasiorek, S., Radnovic, M. (2022). Billiard Ordered Games and Books. Regular and Chaotic Dynamics, 27(2), 132-150. [More Information]
  • Dragovic, V., Gasiorek, S., Radnovic, M. (2022). Integrable billiards on the Minkowski hyperboloid: extremal polynomials and topology. Sbornik Mathematics, 213(9), 34-69. [More Information]

2021

  • Gasiorek, S., Radnovic, M. (2021). Pseudo-Euclidean billiards within confocal curves on the hyperboloid of one sheet. Journal of Geometry and Physics, 161, 104032. [More Information]

2020

  • Dragovic, V., Radnovic, M., Ranomenjanahary, R. (2020). Pencils of Quadrics, Billiard Double-Reflection and Confocal Incircular Nets. In Ron Donagi and Tony Shaska (Eds.), Integrable Systems and Algebraic Geometry, (pp. 133-166). Cambridge: Cambridge University Press. [More Information]
  • Dragovic, V., Radnovic, M. (2020). Periodic Trajectories of Ellipsoidal Billiards in the 3-Dimensional Minkowski Space. In Frank Nijhoff, Yang Shi, Da-Jun Zhang (Eds.), Asymptotic, Algebraic and Geometric Aspects of Integrable Systems, (pp. 159-174). Cham: Springer. [More Information]

2019

  • Joshi, N., Radnovic, M. (2019). Asymptotic behaviour of the third Painleve transcendents in the space of initial values. Transactions of the American Mathematical Society, 372(9), 6507-6546. [More Information]
  • Dragovic, V., Radnovic, M. (2019). Caustics of Poncelet Polygons and Classical Extremal Polynomials. Regular and Chaotic Dynamics, 24(1), 1-35. [More Information]
  • Adabrah, A., Dragovic, V., Radnovic, M. (2019). Elliptical Billiards in the Minkowski Plane and Extremal Polynomials. Russian Journal of Nonlinear Dynamics, 15(4), 397-407. [More Information]

2018

  • Joshi, N., Radnovic, M. (2018). Asymptotic behaviour of the fifth Painleve transcendents in the space of initial values. Proceedings of the London Mathematical Society, 3(116), 1329-1364. [More Information]

2017

  • Dragovic, V., Radnovic, M. (2017). Topological Invariants for Elliptical Billiards and Geodesics on Ellipsoids in the Minkowski Space. Journal of Mathematical Sciences, 223(6), 686-694. [More Information]

2016

  • Joshi, N., Radnovic, M. (2016). Asymptotic Behavior of the Fourth Painleve Transcendents in the Space of Initial Values. Constructive Approximation, 44(2), 195-231. [More Information]

2015

  • Radnovic, M. (2015). Integrable Lattices of Hyperplanes Related to Billiards Within Confocal Quadrics. Publications de l'Institut Mathématique, 98(112), 25-30. [More Information]
  • Dragovic, V., Radnovic, M. (2015). Periods of Pseudo-Integrable Billiards. Arnold Mathematical Journal, 1(1), 69-73. [More Information]
  • Dragovic, V., Radnovic, M. (2015). Pseudo-integrable billiards and double reflection nets. Russian Mathematical Surveys (Uspekhi Matematicheskikh Nauk), 70(1), 1-31. [More Information]

2014

  • Dragovic, V., Radnovic, M. (2014). Bicentennial of the Great Poncelet Theorem (1813-2013): Current advances. Bulletin of the American Mathematical Society, 51(3), 373-445. [More Information]
  • Dragovic, V., Radnovic, M. (2014). Pseudo-integrable billiards and arithmetic dynamics. Journal of Modern Dynamics, 8(1), 109-132. [More Information]

2013

  • Dragovic, V., Radnovic, M. (2013). Minkowski Plane, Confocal Conics and Billiards. Publications de l'Institut Mathématique, 94(108), 17-30. [More Information]

2012

  • Dragovic, V., Radnovic, M. (2012). Billiard algebra, integrable line congruences, and double reflection nets. Journal Of Nonlinear Mathematical Physics, 19(3), 300-317. [More Information]
  • Dragovic, V., Radnovic, M. (2012). Ellipsoidal billiards in pseudo-Euclidean spaces and relativistic quadrics. Advances in Mathematics, 231(3-4), 1173-1201. [More Information]

2011

  • Dragovic, V., Radnovic, M. (2011). Poncelet Porisms and Beyond: Integrable Billiards, Hyperelliptic Jacobians and Pencils of Quadrics, Frontiers in Mathematics. Basel: Birkhauser (imprint of Springer).

2010

  • Dragovic, V., Radnovic, M. (2010). Integrable billiards and quadrics (in Russian). Russian Mathematical Surveys (Uspekhi Matematicheskikh Nauk), 65(2), 319-379. [More Information]
  • Dragovic, V., Radnovic, M. (2010). Integrable Billiards, Quadrics, and Higher-dimensional Poncelet Porisms (in Russian). Moscow-Izhevsk: Regular & Chaotic Dynamics.

2009

  • Dragovic, V., Radnovic, M. (2009). Bifurcations of Liouville Tori in Elliptical Billiards. Regular and Chaotic Dynamics, 14(4-5), 479-494. [More Information]

2008

  • Radnovic, M., Rom-Kedar, V. (2008). Foliations of Isoenergy Surfaces and Singularities of Curves. Regular and Chaotic Dynamics, 13(6), 645-668. [More Information]
  • Dragovic, V., Radnovic, M. (2008). Hyperelliptic Jacobians as billiard algebra of pencils of quadrics: Beyond Poncelet porisms. Advances in Mathematics, 219(5), 1577-1607. [More Information]

2006

  • Dragovic, V., Radnovic, M. (2006). A survey of the analytical description of periodic elliptical billiard trajectories. Journal of Mathematical Sciences, 135(4), 3244-3255.
  • Dragovic, V., Radnovic, M. (2006). Geometry of integrable billiards and pencils of quadrics. Journal de Mathematiques Pures et Appliquees, 85(6), 758-790.

2005

  • Dragovic, V., Radnovic, M. (2005). Corrigendum: "Cayley-type conditions for billiards within k quadrics in Rd". Journal of Physics A: Mathematical and General, 38(36), 7927.

2004

  • Dragovic, V., Radnovic, M. (2004). Cayley-type conditions for billiards within k quadrics in Rd. Journal of Physics A: Mathematical and General, 37(4), 1269-1276.

2003

  • Radnovic, M. (2003). A Note on Billiard Systems in Finsler Plane with Elliptic Indicatrices. Publications de l'Institut Mathématique, 74(87), 7-11.
  • Dragovic, V., Jovanovic, B., Radnovic, M. (2003). On Elliptical Billiardsin the Lobachevsky Space and associated Geodesic Hierarchies. Journal of Geometry and Physics, 47(2-3), 221-234.

1998

  • Dragovic, V., Radnovic, M. (1998). Conditions of Cayley’s Type for Ellipsoidal Billiard. Journal of Mathematical Physics, 39(1), 355-362.
  • Dragovic, V., Radnovic, M. (1998). On periodical trajectories of the billiard systems within an ellipsoid in Rd and generalized Cayley’s condition. Journal of Mathematical Physics, 39(11), 5866-5869.

Selected Grants

2019

  • Geometric analysis of nonlinear systems, Joshi N, Radnovic M, Australian Research Council (ARC)/Discovery Projects (DP)
  • Billiards within confocal quadrics and beyond, Radnovic M, Australian Research Council (ARC)/Discovery Projects (DP)