Displaying similar documents to “Mixing properties of nearly maximal entropy measures for ℤ d shifts of finite type”

Entropy of eigenfunctions of the Laplacian in dimension 2

Gabriel Rivière (2010)

Journées Équations aux dérivées partielles

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We study asymptotic properties of eigenfunctions of the Laplacian on compact Riemannian surfaces of Anosov type (for instance negatively curved surfaces). More precisely, we give an answer to a question of Anantharaman and Nonnenmacher [] by proving that the Kolmogorov-Sinai entropy of a semiclassical measure μ for the geodesic flow g t is bounded from below by half of the Ruelle upper bound. (This text has been written for the proceedings of the 37 èmes Journées EDP (Port d’Albret-June, 7-11...

Puzzles of Quasi-Finite Type, Zeta Functions and Symbolic Dynamics for Multi-Dimensional Maps

Jérôme Buzzi (2010)

Annales de l’institut Fourier

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Entropy-expanding transformations define a class of smooth dynamics generalizing interval maps with positive entropy and expanding maps. In this work, we build a symbolic representation of those dynamics in terms of puzzles (in Yoccoz’s sense), thus avoiding a connectedness condition, hard to satisfy in higher dimensions. Those puzzles are controled by a «constraint entropy» bounded by the hypersurface entropy of the aforementioned transformations. The analysis of those puzzles...

Large time behaviour of a class of solutions of second order conservation laws

Jan Goncerzewicz, Danielle Hilhorst (2000)

Banach Center Publications

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% We study the large time behaviour of entropy solutions of the Cauchy problem for a possibly degenerate nonlinear diffusion equation with a nonlinear convection term. The initial function is assumed to have bounded total variation. We prove the convergence of the solution to the entropy solution of a Riemann problem for the corresponding first order conservation law.

Dynamical entropy of a non-commutative version of the phase doubling

Johan Andries, Mieke De Cock (1998)

Banach Center Publications

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A quantum dynamical system, mimicking the classical phase doubling map z ↦ z 2 on the unit circle, is formulated and its ergodic properties are studied. We prove that the quantum dynamical entropy equals the classical value log2 by using compact perturbations of the identity as operational partitions of unity.

Entropy solution for anisotropic reaction-diffusion-advection systems with L data.

Mostafa Bendahmane, Mazen Saad (2005)

Revista Matemática Complutense

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In this paper, we study the question of existence and uniqueness of entropy solutions for a system of nonlinear partial differential equations with general anisotropic diffusivity and transport effects, supplemented with no-flux boundary conditions, modeling the spread of an epidemic disease through a heterogeneous habitat.