Associate Professor Milena Radnovic
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.
Timetable
(The Weizmann Institute of Science, Rehovot) Postodoctoral Fellow from 2004 to 2007, supervised by Vered Rom-Kedar. | |
(The Abdus Salam ICTP, Trieste) Junior Associate from 2008 to 2014, supervised by Stefano Luzzatto. | |
(African Institute for Mathematical Sciences, Dakar-Mbour) In schoolyear 2012/2013, supervised work on two master theses. The co-supervisor was Abdoul Salam Diallo. | |
(Mathematical Institute SANU, Belgrade) Working as a researcher at the Mathematical Institute SANU since 1997. Associate Research Professor since 2010. Currently at leave. | |
(University of Texas at Dallas) Long term collaboration with Vladimir Dragovic, my original PhD supervisor, on problems surrounding Poncelet theorem, elliptical billiards and geometry of confocal quadrics. |
Project title | Research student |
---|---|
Billiard Dynamics in Projective Spaces Over Fields with Finite Characteristics | Harry HIATT |
Selected publications
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)