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Linearization of Normally Hyperbolic Diffeomorphisms and Flows

C. PUGH, M. SHUB (1970)

Inventiones mathematicae

Li-Yorke pairs of full Hausdorff dimension for some chaotic dynamical systems

J. Neunhäuserer (2010)

Mathematica Bohemica

We show that for some simple classical chaotic dynamical systems the set of Li-Yorke pairs has full Hausdorff dimension on invariant sets.

Local density of diffeomorphisms with large centralizers

Christian Bonatti, Sylvain Crovisier, Gioia M. Vago, Amie Wilkinson (2008)

Annales scientifiques de l'École Normale Supérieure

Given any compact manifold $M$ , we construct a non-empty open subset $𝒪$ of the space ${Diff}^{1} (M)$ of $C^{1}$ -diffeomorphisms and a dense subset $𝒟 \subset 𝒪$ such that the centralizer of every diffeomorphism in $𝒟$ is uncountable, hence non-trivial.

Local dimensions for Poincaré recurrences.

Afraimovich, Valentin, Chazottes, Jean-René, Saussol, Benoît (2000)

Electronic Research Announcements of the American Mathematical Society [electronic only]

Local Groups of Differentiable Transformations.

J.R. DORROH (1971)

Mathematische Annalen

Local Lyapunov exponents and a local estimate of Hausdorff dimension

Alp Eden (1989)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Local rigidity of actions of higher rank abelian groups and KAM method.

Damjanović, Danijela, Katok, Anatole (2004)

Electronic Research Announcements of the American Mathematical Society [electronic only]

Local structural stability of $C^{2}$ integrable 1-forms

Alcides Lins Neto (1977)

Annales de l'institut Fourier

In this work we consider a class of germs of singularities of integrable 1-forms in $R^{n}$ which are structurally stable in class $C^{r}$ ( $r \geq 2$ if $n = 3$ , $r \geq 4$ if $n \geq 4$ ), whose 1-jet is zero at the singularity. In this class the stability depends essentially on the fact that the perturbations allowed are integrable.

Localization of periodic orbits of autonomous systems based on high-order extremum conditions.

Starkov, Konstantin E. (2004)

Mathematical Problems in Engineering

Locally equicontinuous dynamical systems

Eli Glasner, Benjamin Weiss (2000)

Colloquium Mathematicae

A new class of dynamical systems is defined, the class of “locally equicontinuous systems” (LE). We show that the property LE is inherited by factors as well as subsystems, and is closed under the operations of pointed products and inverse limits. In other words, the locally equicontinuous functions in $l_{\infty} (ℤ)$ form a uniformly closed translation invariant subalgebra. We show that WAP ⊂ LE ⊂ AE, where WAP is the class of weakly almost periodic systems and AE the class of almost equicontinuous systems....