N. Simányi

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19962025

most citedProof of the Boltzmann-Sinai Ergodic Hypothesis for Typical Hard Disk Systems

63 citations · 266 across the 27 of their papers we have counts for

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math.DS2025

Asymptotic Homotopical Complexity of an Infinite Sequence of Dispersing $2 D$ Billiards

Nandor Simanyi

We investigate the large scale chaotic, topological structure of the trajectories of an infinite sequence of dispersing, hence ergodic, $2 D$ billiards with the configuration space…

math.DS2024

Proof of Wojtkowski's Falling Particle Conjecture

Nandor Simanyi

In this paper we present an unconditional proof of Wojtkowski's Ergodicity Conjecture for almost every system of 1D perfectly elastic balls falling down in a half line under consta…

math.DS2022

Conditional Proof of the Ergodic Conjecture for Falling Ball Systems

Nandor Simanyi

In this paper we present a conditional proof of Wojtkowski's Ergodicity Conjecture for the system of 1D perfectly elastic balls falling down in a half line under constant gravitati…

math.DS2016

Homotopical Complexity of a Billiard Flow on the 3D Flat Torus with Two Cylindrical Obstacles

Caleb C. Moxley, Nandor J. Simanyi

We study the homotopical rotation vectors and the homotopical rotation sets for the billiard flow on the unit flat torus with two, disjoint and orthogonal cylindrical scatterers re…

math.DS2016

Homotopical Complexity of a 3D Billiard Flow

Caleb C. Moxley, Nandor J. Simanyi

In this paper we study the homotopical rotation vectors and the homotopical rotation sets for the billiard flow on the unit flat torus with three, mutually intersecting and mutuall…

math.DS2015★ 1 cited

Further Developments of Sinai's Ideas: The Boltzmann-Sinai Hypothesis

Nandor Simanyi

In 1963 Ya. G. Sinai formulated a modern version of Boltzmann's ergodic hypothesis, what we now call the ``Boltzmann-Sinai Ergodic Hypothesis'': The billiard system of $N$ ($N\ge 2…

math.DS2012★ 6 cited

Singularities and nonhyperbolic manifolds do not coincide

Nandor Simanyi

We consider the billiard flow of elastically colliding hard balls on the flat $ν$ -torus ( $ν \geq 2$ ), and prove that no singularity manifold can even locally coincide with a manifold…

math.DS2010

Homotopical Complexity of 2D Billiard Orbits

Lee M. Goswick, Nandor Simanyi

Traditionally, rotation numbers for toroidal billiard flows are defined as the limiting vectors of average displacements per time on trajectory segments. The billard trajectories,…

math.DS2010★ 3 cited

The Boltzmann--Sinai Ergodic Hypothesis In Full Generality

Nandor Simanyi

In the ergodic theory of semi-dispersing billiards the Local Ergodic Theorem, proved by Chernov and Sinai in 1987, plays a central role. So far, all existing proofs of this theorem…

math.DS2008★ 17 cited

Unconditional Proof of the Boltzmann-Sinai Ergodic Hypothesis

Nandor Simanyi

We consider the system of $N$ ( $\geq 2$ ) elastically colliding hard balls of masses $m_{1}, ..., m_{N}$ and radius $r$ on the flat unit torus $T^{ν}$ , $ν \geq 2$ . We prove the so called Bo…

math.DS2007

An Effective Contraction Estimate in the Stable Subspaces of Phase Points in Hard Ball Systems

Nandor Simanyi

In this paper we prove the following result, useful and often needed in the study of the ergodic properties of hard ball systems: In any such system, for any phase point x with a n…

math.DS2006

Homotopical Rotation Numbers of 2D Billiards

Lee M. Goswick, Nandor Simanyi

Traditionally, rotation numbers for toroidal billiard flows are defined as the limiting vectors of average displacements per time on trajectory segments. Naturally, these creatures…

math.DS2006★ 17 cited

Conditional Proof of the Boltzmann-Sinai Ergodic Hypothesis

Nandor Simanyi

We consider the system of $N$ ( $\geq 2$ ) elastically colliding hard balls of masses $m_{1}, ..., m_{N}$ and radius $r$ on the flat unit torus $T^{ν}$ , $ν \geq 2$ . We prove the so called Bo…

math.DS2006★ 4 cited

Flow-invariant hypersurfaces in semi-dispersing billiards

N. Chernov, N. Simanyi

This work results from our attempts to solve Boltzmann-Sinai's hypothesis about the ergodicity of hard ball gases. A crucial element in the studies of the dynamics of hard balls is…

math.DS2005★ 1 cited

The Boltzmann-Sinai Ergodic Hypothesis in Full Generality (Without Exceptional Models)

Nandor Simanyi

We consider the system of $N$ ( $\geq 2$ ) elastically colliding hard balls of masses $m_{1}, ..., m_{N}$ and radius $r$ on the flat unit torus $T^{ν}$ , $ν \geq 2$ . We prove the so called Bo…

math.DS2005★ 13 cited

Rotation sets of billiards with one obstacle

A. Blokh, M. Misiurewicz, N. Simanyi

We investigate the rotation sets of billiards on the $m$ -dimensional torus with one small convex obstacle and in the square with one small convex obstacle. In the first case the di…

math.DS2004★ 2 cited

The Boltzmann-Sinai Ergodic Hypothesis in Two Dimensions (Without Exceptional Models)

Nandor Simanyi

We consider the system of $N$ ( $\geq 2$ ) elastically colliding hard balls of masses $m_{1}, ..., m_{N}$ and radius $r$ in the flat unit torus $T^{ν}$ , $ν \geq 2$ . In the case $ν = 2$ we prov…

math.DS2003★ 1 cited

Improvement of the Theorem on Local Ergodicity

Nandor Simanyi

We prove here that in the Theorem on Local Ergodicity for Semi-Dispersive Billiards (proved by N. I. Chernov and Ya. G. Sinai in 1987) the recently added condition (by P. Bálint, N…

math.DS2003

Upgrading the Theorem on Local Ergodicity

Nandor Simanyi

We prove here that in the Theorem on Local Ergodicity for Semi-Dispersive Billiards (proved by N. I. Chernov and Ya. G. Sinai in 1987) the condition of the so called ``Ansatz'' can…

math.DS2002★ 48 cited

Proof of the Ergodic Hypothesis for Typical Hard Ball Systems

Nandor Simanyi

We consider the system of $N$ ( $\geq 2$ ) hard balls with masses $m_{1}, ..., m_{N}$ and radius $r$ in the flat torus $T_{L}^{ν} = R^{ν} / L \cdot Z^{ν}$ of size $L$ , $ν \geq 3$ . We prove the…

math.DS2002

Proving The Ergodic Hypothesis for Billiards With Disjoint Cylindric Scatterers

Nandor Simanyi

In this paper we study the ergodic properties of mathematical billiards describing the uniform motion of a point in a flat torus from which finitely many, pairwise disjoint, tubula…

math.DS2000★ 63 cited

Proof of the Boltzmann-Sinai Ergodic Hypothesis for Typical Hard Disk Systems

Nandor Simanyi

We consider the system of $N$ ( $\geq 2$ ) hard disks of masses $m_{1}, ..., m_{N}$ and radius $r$ in the flat unit torus $T^{2}$ . We prove the ergodicity (actually, the B-mixing property…

math.DS1999★ 14 cited

The Complete Hyperbolicity of Cylindric Billiards

Nandor Simanyi

The connected configuration space of a so called cylindric billiard system is a flat torus minus finitely many spherical cylinders. The dynamical system describes the uniform motio…

math.DS1997★ 29 cited

Ergodicity of hard spheres in a box

Nandor Simanyi

We prove that the system of two hard balls in a $ν$ -dimensional ( $ν \geq 2$ ) rectangular box is ergodic and, therefore, actually it is a Bernoulli flow.

Asymptotic Homotopical Complexity of an Infinite Sequence of Dispersing 2D Billiards

Proof of Wojtkowski's Falling Particle Conjecture

Conditional Proof of the Ergodic Conjecture for Falling Ball Systems

Homotopical Complexity of a Billiard Flow on the 3D Flat Torus with Two Cylindrical Obstacles

Homotopical Complexity of a 3D Billiard Flow

Further Developments of Sinai's Ideas: The Boltzmann-Sinai Hypothesis

Singularities and nonhyperbolic manifolds do not coincide

Homotopical Complexity of 2D Billiard Orbits

The Boltzmann--Sinai Ergodic Hypothesis In Full Generality

Unconditional Proof of the Boltzmann-Sinai Ergodic Hypothesis

An Effective Contraction Estimate in the Stable Subspaces of Phase Points in Hard Ball Systems

Homotopical Rotation Numbers of 2D Billiards

Conditional Proof of the Boltzmann-Sinai Ergodic Hypothesis

Flow-invariant hypersurfaces in semi-dispersing billiards

The Boltzmann-Sinai Ergodic Hypothesis in Full Generality (Without Exceptional Models)

Rotation sets of billiards with one obstacle

The Boltzmann-Sinai Ergodic Hypothesis in Two Dimensions (Without Exceptional Models)

Improvement of the Theorem on Local Ergodicity

Upgrading the Theorem on Local Ergodicity

Proof of the Ergodic Hypothesis for Typical Hard Ball Systems

Proving The Ergodic Hypothesis for Billiards With Disjoint Cylindric Scatterers

Proof of the Boltzmann-Sinai Ergodic Hypothesis for Typical Hard Disk Systems

The Complete Hyperbolicity of Cylindric Billiards

Ergodicity of hard spheres in a box

Asymptotic Homotopical Complexity of an Infinite Sequence of Dispersing $2 D$ Billiards