63 citations · 266 across the 27 of their papers we have counts for
29 papers
Asymptotic Homotopical Complexity of an Infinite Sequence of Dispersing Billiards
Nandor Simanyi
We investigate the large scale chaotic, topological structure of the trajectories of an infinite sequence of dispersing, hence ergodic, billiards with the configuration space…
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…
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…
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…
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…
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\ge 2…
Renyi's Parking Problem Revisited
Matthew P. Clay, Nandor J. Simanyi
Rényi's parking problem (or sequential interval packing problem) dates back to 1958, when Rényi studied the following random process: Consider an interval of length , a…
Singularities and nonhyperbolic manifolds do not coincide
Nandor Simanyi
We consider the billiard flow of elastically colliding hard balls on the flat -torus (), and prove that no singularity manifold can even locally coincide with a manifold…
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,…
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…
Sums of squares and orthogonal integral vectors
Lee M. Goswick, Emil W. Kiss, Gabor Moussong +1
Two vectors in $\BZ^3$ are called \emph{twins} if they are orthogonal and have the same length. The paper describes twin pairs using cubic lattices, and counts the number of twin p…
Unconditional Proof of the Boltzmann-Sinai Ergodic Hypothesis
Nandor Simanyi
We consider the system of () elastically colliding hard balls of masses and radius on the flat unit torus , . We prove the so called Bo…
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…
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…
Conditional Proof of the Boltzmann-Sinai Ergodic Hypothesis
Nandor Simanyi
We consider the system of () elastically colliding hard balls of masses and radius on the flat unit torus , . We prove the so called Bo…
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…
The Boltzmann-Sinai Ergodic Hypothesis in Full Generality (Without Exceptional Models)
Nandor Simanyi
We consider the system of () elastically colliding hard balls of masses and radius on the flat unit torus , . We prove the so called Bo…
Rotation sets of billiards with one obstacle
A. Blokh, M. Misiurewicz, N. Simanyi
We investigate the rotation sets of billiards on the -dimensional torus with one small convex obstacle and in the square with one small convex obstacle. In the first case the di…
A Note on the Size of the Largest Ball Inside a Convex Polytope
Imre Barany, Nandor Simanyi
Let be an integer, the set of all unit vectors of pointing in the direction of a nonzero integer vector of the cube . Denote by the radius o…
The Boltzmann-Sinai Ergodic Hypothesis in Two Dimensions (Without Exceptional Models)
Nandor Simanyi
We consider the system of () elastically colliding hard balls of masses and radius in the flat unit torus , . In the case we prov…
On the complexity of curve fitting algorithms
N. Chernov, C. Lesort, N. Simanyi
We study a popular algorithm for fitting polynomial curves to scattered data based on the least squares with gradient weights. We show that sometimes this algorithm admits a substa…
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…
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…
Proof of the Ergodic Hypothesis for Typical Hard Ball Systems
Nandor Simanyi
We consider the system of () hard balls with masses and radius in the flat torus of size , . We prove the…