On the pseudo orbit tracing property and its relationship to stability
Peter Walters
- pp 231-244
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The article was published on 1978-01-01 and is currently open access. It has received 231 citations till now. The article focuses on the topics: Orbit (control theory) & Topological entropy.read more
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Pseudo-orbit shadowing in the family of tent maps
TL;DR: In this article, it is shown that les applications en tente ont la propriete d'ombrage for presque tous les parametres s, mais elles n'ont pas cette propriete pour un ensemble dense non denombrable des parametre.
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Lyapunov functions and topological stability
TL;DR: Theorem 2.1 in this paper shows that a diffeomorphism f of a compact riemannian manifold M is Anosov if and only if its tangent map has a non-degenerate Lyapunov quadratic function.
OtherDOI
A panorama of specification-like properties and their consequences
TL;DR: In this paper, the authors examine relations between specification-like prop- erties and such notions as mixing, entropy, the structure of the simplex of invariant measures, and various types of shadowing property.
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On topological dynamics of Turing machines
TL;DR: In both classes it is shown that a bijective expansive TMT is conjugate to a subshift of finite type and that topological entropy of every TMH is zero, and conjecture that every TMT has a periodic point.
References
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Equilibrium states and the ergodic theory of Anosov diffeomorphisms
TL;DR: Gibbs Measures and Gibbs measures have been used in this article to define Axiom a Diffeomorphisms for general Thermodynamic Formalism and Ergodic Theory of Axiom-a-Diffeomorphism.
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