Displaying similar documents to “Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows”

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...

On the orbit of the centralizer of a matrix

Ching-I Hsin (2002)

Colloquium Mathematicae

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Let A be a complex n × n matrix. Let A' be its commutant in Mₙ(ℂ), and C(A) be its centralizer in GL(n,ℂ). Consider the standard C(A)-action on ℂⁿ. We describe the C(A)-orbits via invariant subspaces of A'. For example, we count the number of C(A)-orbits as well as that of invariant subspaces of A'.