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pro vyhledávání: '"measure of maximal entropy"'
Autor:
Kim, Dongryul M., Oh, Hee
For a geometrically finite Kleinian group $\Gamma$, the Bowen-Margulis-Sullivan measure is finite and is the unique measure of maximal entropy for the geodesic flow, as shown by Sullivan and Otal-Peign\'e respectively. Moreover, it is strongly mixing
Externí odkaz:
http://arxiv.org/abs/2404.09745
Publikováno v:
Ann. H. Lebesgue 7 (2024) 727-747
Using recent work of Carrand on equilibrium states for the billiard map, and bootstrapping via a "leapfrogging" method from a previous article of Baladi and Demers, we construct the unique measure of maximal entropy for two-dimensional finite horizon
Externí odkaz:
http://arxiv.org/abs/2209.00982
Autor:
Demers, Mark F., Korepanov, Alexey
In a recent work, Baladi and Demers constructed a measure of maximal entropy for finite horizon dispersing billiard maps and proved that it is unique, mixing and moreover Bernoulli. We show that this measure enjoys natural probabilistic properties fo
Externí odkaz:
http://arxiv.org/abs/2204.04684
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Autor:
Makienko, Peter, Cabrera, Carlos
We compare dynamical and algebraic properties of semigroups of rational maps. In particular, we show a version of the Day-von Neumann's conjecture and give a partial positive answer to "Sushkievich's problem" for semigroups of rational maps. We also
Externí odkaz:
http://arxiv.org/abs/2109.11601
Autor:
Demers, Mark F.
For a class of piecewise hyperbolic maps in two dimensions, we propose a combinatorial definition of topological entropy by counting the maximal, open, connected components of the phase space on which iterates of the map are smooth. We prove that thi
Externí odkaz:
http://arxiv.org/abs/2001.10068
Autor:
Pakovich, Fedor
Let $P_1,P_2,\dots, P_k$ be complex polynomials of degree at least two that are not simultaneously conjugate to monomials or to Chebyshev polynomials, and $S$ the semigroup under composition generated by $P_1,P_2,\dots, P_k$. We show that all element
Externí odkaz:
http://arxiv.org/abs/2009.12261
We show that the measure of maximal entropy for the hereditary closure of a $\mathscr{B}$-free subshift has the Gibbs property if and only if the Mirsky measure of the subshift is purely atomic. This answers an open question asked by Peckner. Moreove
Externí odkaz:
http://arxiv.org/abs/2004.07643
Autor:
Obata, Davi
In this paper we prove that for sufficiently large parameters the standard map has a unique measure of maximal entropy (m.m.e.). Moreover, we prove: the m.m.e. is Bernoulli, and the periodic points with Lyapunov exponents bounded away from zero equid
Externí odkaz:
http://arxiv.org/abs/2003.00236
Autor:
Pakovich, Fedor
We show that describing rational functions $f_1,$ $f_2,$ $\dots,f_n$ sharing the measure of maximal entropy reduces to describing solutions of the functional equation $A\circ X_1=A\circ X_2=\dots=A\circ X_n$ in rational functions. We also provide som
Externí odkaz:
http://arxiv.org/abs/1910.07363