Symbolic extensions and smooth dynamical systems

By Tomasz Downarowicz, S. Newhouse. 2005

99 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fa0bb3d5965b91baf2611b898bcd731b6e35627d

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In Analytical Chemistry

In Mathematical Physics

Citations in the corpus

The Entropy Conjecture for Diffeomorphisms away from Tangencies (2010, result): “This is in contrast with previous work of Downarwicz, Newhouse [12], based on the theory developed by Boyle, Downarwicz [5], where it is shown that nonexistence of symbolic extensions is typical on the closure of the set of area preserving diffeomorphisms with homoclinic tangencies.”
FIFTY YEARS OF ENTROPY IN DYNAMICS: 1958-2007 (2007, background): “Downarowicz, Newhouse and others [19, 24], as well as detailed analysis of maximal entropy measures in low dimension by Buzzi.”
Measures of maximal entropy for surface diffeomorphisms (2018, background): “A standard construction produces infinitely many disjoint horseshoes with topological entropy bounded away from zero, by a Cr-perturbation near a homoclinic orbit (see for instance [62, 65, 43, 30]).”
The entropy theory of symbolic extensions (2004, methodology): “The results of this paper are required for the Downarowicz-Newhouse results [ DN ] on smooth dynamical systems.”
Entropy in dynamical systems (2003, background): “1 [Downarowicz and Newhouse, 2005] Let T be a C transformation of a compact Riemannian manifold M of dimension dim, with r > 1.”
On Stochastic Sea of the Standard Map (2010, background): “ equal to the dimension of the ambient manifold. Therefore it is reasonable to ask rst whether those invariant sets indeed have full Hausdor dimension. In dissipative setting Downarowicz and Newhouse [DN] proved that there is a residual subset Rof the space of Cr-dieomorphisms of a compact two dimen”
Abundance of C 1 -robust homoclinic tangencies (2009, background): “A homoclinic tangency is a dynamical mechanism which is at the heart of a great variety of non-hyperbolic phenomena: persistent coexistence of infinitely many sinks [22], Hénon-like strange attractors [5, 20], super-exponential growth of the number of periodic points [19], and non-existence of symbo”
Hyperbolic sets exhibiting ¹-persistent homoclinic tangency for higher dimensions (2007, methodology): “In [5], Downarowicz and Newhouse showed that any C(1)-generic area-preserving diffeomorphism of a closed surface is either an Anosov diffeomorphism or has no symbolic extension.”