Displaying similar documents to “How restrictive is topological dynamics?”

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...

Orbit Structure of certain ℝ 2 -actions on solid torus

C. Maquera, L. F. Martins (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

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In this paper we describe the orbit structure of   C 2 -actions of   ℝ 2   on the solid torus   S 1 × D 2   having   S 1 × { 0 }   and   S 1 × ∂ D 2   as the only compact orbits, and   S 1 × { 0 }   as singular set.

Reidemeister orbit sets

Boju Jiang, Seoung Ho Lee, Moo Ha Woo (2004)

Fundamenta Mathematicae

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The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, much as the Reidemeister set does in Nielsen fixed point theory. Extending Ferrario's work on Reidemeister sets, we obtain algebraic results such as addition formulae for Reidemeister orbit sets. Similar formulae for Nielsen type essential orbit numbers are also proved for fibre preserving maps.