Nandor Simanyi

Nandor Simanyi
Professor

Professor (P), Mathematics , College of Arts and Sciences

Overview

I am a professor of mathematics at the University of Alabama at Birmingham.

Selected Publications

Academic Article

Year	Title	Altmetric
2019	Homotopical complexity of a billiard flow on the 3D flat torus with two cylindrical obstacles. Ergodic Theory and Dynamical Systems. 39:1071-1081. 2019
2017	Homotopical complexity of a 3D billiard flow. Contemporary Mathematics. 698:169-180. 2017
2016	Rényi's parking problem revisited. Stochastics and Dynamics. 16. 2016
2015	Further Developments of Sinai's Ideas: The Boltzmann-Sinai Hypothesis 2015
2013	Singularities and non-hyperbolic manifolds do not coincide. Nonlinearity. 26:1703-1717. 2013
2012	Stable rgimes for hard disks in a channel with twisting walls 2012
2012	Sums of squares and orthogonal integral vectors. Journal of Number Theory. 132:37-53. 2012
2011	Homotopical complexity of 2D billiard orbits. Studia Scientiarum Mathematicarum Hungarica. 48:540-562. 2011
2011	Circle decompositions of surfaces 2011
2010	The Boltzmann--Sinai Ergodic Hypothesis In Full Generality 2010
2010	Upgrading the Local Ergodic Theorem for planar semi-dispersing billiards. Journal of Statistical Physics. 139:355-366. 2010
2009	Conditional proof of the boltzmann-Sinai ergodic hypothesis. Inventiones Mathematicae. 177:381-413. 2009
2008	Unconditional Proof of the Boltzmann-Sinai Ergodic Hypothesis 2008
2007	Flow-invariant hypersurfaces in semi-dispersing billiards 2007
2007	An Effective Contraction Estimate in the Stable Subspaces of Phase Points in Hard Ball Systems 2007
2006	Homotopical Rotation Numbers of 2D Billiards 2006
2006	Rotation sets of billiards with one obstacle. Communications in Mathematical Physics. 266:239-265. 2006
2005	A note on the size of the largest ball inside a convex polytope. Periodica Mathematica Hungarica. 51:15-18. 2005
2005	The Boltzmann-Sinai Ergodic Hypothesis in Full Generality (Without Exceptional Models) 2005
2004	The Boltzmann-Sinai Ergodic Hypothesis in Two Dimensions (Without Exceptional Models) 2004
2004	Proof of the ergodic hypothesis for typical hard ball systems 2004
2004	On the complexity of curve fitting algorithms. Journal of Complexity. 20:484-492. 2004
2004	Proving the ergodic hypothesis for billiards with disjoint cylindric scatterers. Nonlinearity. 17:1-21. 2004
2003	Improvement of the Theorem on Local Ergodicity 2003
2003	Upgrading the Theorem on Local Ergodicity 2003
2003	On the complexity of curve fitting algorithms 2003
2003	Proof of the Boltzmann-Sinai ergodic hypothesis for typical hard disk systems. Inventiones Mathematicae. 154:123-178. 2003
2002	The complete hyperbolicity of cylindric billiards. Ergodic Theory and Dynamical Systems. 22:281-302. 2002
2000	Non-integrability of cylindric billiards and transitive Lie group actions. Ergodic Theory and Dynamical Systems. 20:593-610. 2000
1999	Ergodicity of hard spheres in a box. Ergodic Theory and Dynamical Systems. 19:741-766. 1999
1999	Hard ball systems are completely hyperbolic. Annals of Mathematics. 149:35-96. 1999
1996	The Boltzmann-Sinai Ergodic Hypothesis for Hard Ball Systems 1996
1996	The characteristic exponents of the falling ball model. Communications in Mathematical Physics. 182:457-468. 1996
1995	The K-property of Hamiltonian systems with restricted hard ball interactions. Mathematical Research Letters. 2:751-770. 1995
1994	The K-property of 4D billiards with nonorthogonal cylindric scatterers. Journal of Statistical Physics. 76:587-604. 1994
1992	The K-property of N billiard balls I. Inventiones Mathematicae. 108:521-548. 1992
1992	The K-property of N billiard balls II. Computation of neutral linear spaces. Inventiones Mathematicae. 110:151-172. 1992
1992	The K-property of four billiard balls. Communications in Mathematical Physics. 144:107-148. 1992
1992	Dual polygonal billiards and necklace dynamics. Communications in Mathematical Physics. 143:431-449. 1992
1991	A "transversal" fundamental theorem for semi-dispersing billiards. Communications in Mathematical Physics. 138:207-208. 1991
1991	The K-Property of Three Billiard Balls. Annals of Mathematics. 133:37. 1991
1990	A "Transversal" Fundamental Theorem for semi-dispersing billiards. Communications in Mathematical Physics. 129:535-560. 1990
1989	Dispersing billiards without focal points on surfaces are ergodic. Communications in Mathematical Physics. 125:439-457. 1989
1989	Ergodic properties of semi-dispersing billiards. I. Two cylindric scatterers in the 3D torus. Nonlinearity. 2:311-326. 1989
1989	Two-particle billiard system with arbitrary mass ratio. Ergodic Theory and Dynamical Systems. 9:165-171. 1989
1987	Heat conduction in caricature models of the Lorentz gas. Journal of Statistical Physics. 46:303-318. 1987
1986	Random walks with internal degrees of freedom - III. Stationary probabilities. Probability Theory and Related Fields. 72:603-617. 1986

Research Overview

Ergodic theory and dynamical systems with particular emphasis on hyperbolic dynamical systems with singularities, like mathematical billiards.

Principal Investigator On

Dynamical Models for Superdiffusion and Superconductivity awarded by NSF - National Science Foundation

Ergodic Properties of Mathematical Billiards awarded by NSF - National Science Foundation

Teaching Overview

I teach mostly advanced undergraduate courses, like Linear Algebra, Ordinary Differential Equstions, Partial Differential Equations, Probability, and graduate courses like Abstract Algebra, Advanced Probability, Advanced Statistics, Topology, etc.