Related papers: Measure of maximal entropy for finite horizon Sina…
The semiclassical theory for billiards with mixed boundary conditions is developed and explicit expressions for the smooth and the oscillatory parts of the spectral density are derived. The parametric dependence of the spectrum on the…
We study blow-ups around fixed points at Type I singularities of the Ricci flow on closed manifolds using Perelman's W-functional. First, we give an alternative proof of the result obtained by Naber and Enders-M\"{u}ller-Topping that…
Let $Y$ be a topological Markov chain with finite leading and follower sets. Special flow over $Y$ whose height function depends on the time zero of elements of $Y$ is constructed. Then a formula for computing the entropy of this flow will…
Streamlines and distributions of nodal points are used as signatures of chaos in coherent electron transport through three types of billiards, Sinai, Bunimovich and rectangular. Numerical averaged distribution functions of nearest distances…
We find sufficient conditions for bounded density shifts to have a unique measure of maximal entropy. We also prove that every measure of maximal entropy of a bounded density shift is fully supported. As a consequence of this, we obtain…
The present paper aims to investigate the metric mean dimension theory of continuous flows. We introduce the notion of metric mean dimension for continuous flows to characterize the complexity of flows with infinite topological entropy. For…
We show that Lyapunov exponent for the Sinai billiard is $\lambda = -2\log(R)+C+O(R\log^2 R)$ with $C=1-4\log 2+27/(2\pi^2)\cdot \zeta(3)$ where $R$ is the radius of the circular scatterer. We consider the disk-to-disk-map of the standard…
Based on very accurate measurements performed on a superconducting microwave resonator shaped like a desymmetrized three-dimensional (3D) Sinai billiard, we investigate for the first time spectral properties of the vectorial Helmholtz, i.e.…
We prove that any 3-dimensional singular hyperbolic attractor admits for any H\"older continuous potential $V$ at most one equilibrium state for $V$ among regular measures. We give a condition on $V$ which ensures that no singularity can be…
We study the billiard map corresponding to a periodic Lorentz gas in 2-dimensions in the presence of small holes in the table. We allow holes in the form of open sets away from the scatterers as well as segments on the boundaries of the…
We give a method to bound the entropy of measures on $SL_{d}(\mathbb{R})/SL_{d}(\mathbb{Z})$ which are invariant under a one parameter diagonal subgroup, in terms of entropy contributions from the regions of the cusp corresponding to…
The Lorentz gas is a billiard model involving a point particle diffusing deterministically in a periodic array of convex scatterers. In the two dimensional finite horizon case, in which all trajectories involve collisions with the…
We introduce the notion of rescaled expansive measures to study a measure-theoretic formulation of rescaled expansiveness for flows, particularly in the presence of singularities. Equivalent definitions are established via…
We give a criterion which allows to prove non-ergodicity for certain infinite periodic billiards and directional flows on Z-periodic translation surfaces. Our criterion applies in particular to a billiard in an infinite band with…
This paper studies minimal surface entropy (the exponential asymptotic growth of the number of minimal surfaces up to a given value of area) for negatively curved metrics on hyperbolic $3$-manifolds of finite volume, particularly its…
The semiclassical description of billiard spectra is extended to include the diffractive contributions from orbits which are nearly tangent to a concave part of the boundary. The leading correction for an unstable isolated orbit is of the…
We consider polygonal billiards with collisions contracting the reflection angle towards the normal to the boundary of the table. In previous work, we proved that such billiards has a finite number of ergodic SRB measures supported on…
We show how Rio's method [Probab. Theory Related Fields 104 (1996) 255--282] can be adapted to establish a rate of convergence in ${\frac{1}{\sqrt{n}}}$ in the multidimensional central limit theorem for some stationary processes in the…
For any fixed alphabet A, the maximum topological entropy of a Z^d subshift with alphabet A is obviously log |A|. We study the class of nearest neighbor Z^d shifts of finite type which have topological entropy very close to this maximum,…
We investigate the integrability of Kepler billiards-mechanical billiard systems in which a particle moves under the influence of a Keplerian potential and reflects elastically at the boundary of a strictly convex planar domain. Our main…