Statistical properties of type D dispersing billiards
نویسندگان
چکیده
<p style='text-indent:20px;'>We consider dispersing billiard tables whose boundary is piecewise smooth and the free flight function unbounded. We also assume there are no cusps. Such called type D in monograph of Chernov Markarian [<xref ref-type="bibr" rid="b9">9</xref>]. For a class non-degenerate billiards, we prove exponential decay correlation several other statistical properties.</p>
منابع مشابه
Regularity of local manifolds in dispersing billiards
This work is devoted to 2D dispersing billiards with smooth boundary, i.e. periodic Lorentz gases (with and without horizon). We revisit several fundamental properties of these systems and make a number of improvements. The necessity of such improvements became obvious during our recent studies of gases of several particles [CD]. We prove here that local (stable and unstable) manifolds, as well...
متن کاملFlow-Invariant Hypersurfaces in Semi-Dispersing Billiards
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 analysis of special hypersurfaces in the phase space consisting of degenerate trajectories (which lack complete hyperbolicity). We prove that if a flow-invariant hypersurface J in the phase space of a semi-disper...
متن کاملLimit Theorems for Dispersing Billiards with Cusps
Dispersing billiards with cusps are deterministic dynamical systems with a mild degree of chaos, exhibiting “intermittent” behavior that alternates between regular and chaotic patterns. Their statistical properties are therefore weak and delicate. They are characterized by a slow (power-law) decay of correlations, and as a result the classical central limit theorem fails. We prove that a non-cl...
متن کاملSemi-dispersing billiards with an infinite cusp
Let f : [0,+∞) −→ (0,+∞) be a sufficiently smooth convex function, vanishing at infinity. Consider the planar domain Q delimited by the positive x-semiaxis, the positive y-semiaxis, and the graph of f . Under certain conditions on f , we prove that the billiard flow in Q has a hyperbolic structure and, for some examples, that it is also ergodic. This is done using the cross section correspondin...
متن کامل1 Semi - dispersing billiards with an infinite
Let f : [0,+∞) −→ (0,+∞) be a sufficiently smooth convex function, vanishing at infinity. Consider the planar domain Q delimited by the positive x-semiaxis, the positive y-semiaxis, and the graph of f . Under certain conditions on f , we prove that the billiard flow in Q has a hyperbolic structure and, for some examples, that it is also ergodic. This is done using the cross section correspondin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems
سال: 2022
ISSN: ['1553-5231', '1078-0947']
DOI: https://doi.org/10.3934/dcds.2022073