Displaying similar documents to “Regularity of topological and metric entropy of hyperbolic flows.”

On the origin and development of some notions of entropy

Francisco Balibrea (2015)

Topological Algebra and its Applications

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Discrete dynamical systems are given by the pair (X, f ) where X is a compact metric space and f : X → X a continuous maps. During years, a long list of results have appeared to precise and understand what is the complexity of the systems. Among them, one of the most popular is that of topological entropy. In modern applications other conditions on X and f have been considered. For example X can be non-compact or f can be discontinuous (only in a finite number of points and with bounded...

Diastatic entropy and rigidity of complex hyperbolic manifolds

Roberto Mossa (2016)

Complex Manifolds

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Let f : Y → X be a continuous map between a compact real analytic Kähler manifold (Y, g) and a compact complex hyperbolic manifold (X, g0). In this paper we give a lower bound of the diastatic entropy of (Y, g) in terms of the diastatic entropy of (X, g0) and the degree of f . When the lower bound is attained we get geometric rigidity theorems for the diastatic entropy analogous to the ones obtained by G. Besson, G. Courtois and S. Gallot [2] for the volume entropy. As a corollary,when...

The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section

Dietmar Kröner, Philippe G. LeFloch, Mai-Duc Thanh (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider the Euler equations for compressible fluids in a nozzle whose cross-section is variable and may contain discontinuities. We view these equations as a hyperbolic system in nonconservative form and investigate weak solutions in the sense of Dal Maso, LeFloch and Murat [ (1995) 483–548]. Observing that the entropy equality has a fully conservative form, we derive a minimum entropy principle satisfied by entropy solutions. We then establish the stability of a...