Displaying similar documents to “There arc uncountably many homeomorphism types of orbits in flows”

Periodic orbits and chain-transitive sets of C1-diffeomorphisms

Sylvain Crovisier (2006)

Publications Mathématiques de l'IHÉS

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We prove that the chain-transitive sets of C-generic diffeomorphisms are approximated in the Hausdorff topology by periodic orbits. This implies that the homoclinic classes are dense among the chain-recurrence classes. This result is a consequence of a global connecting lemma, which allows to build by a C-perturbation an orbit connecting several prescribed points. One deduces a weak shadowing property satisfied by C-generic diffeomorphisms: any pseudo-orbit is approximated in the Hausdorff...

How restrictive is topological dynamics?

Anzelm Iwanik (1997)

Commentationes Mathematicae Universitatis Carolinae

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Let T be a permutation of an abstract set X . In ZFC, we find a necessary and sufficient condition it terms of cardinalities of the T -orbits that allows us to topologize ( X , T ) as a topological dynamical system on a compact Hausdorff space. This extends an early result of H. de Vries concerning compact metric dynamical systems. An analogous result is obtained for 𝐙 2 -actions without periodic points.

Locally equicontinuous dynamical systems

Eli Glasner, Benjamin Weiss (2000)

Colloquium Mathematicae

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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 ∞ ( 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...