Displaying similar documents to “Shadowing lemma for family of ε -trajectories”

Poincaré-Hopf index and partial hyperbolicity

C. A Morales (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

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We use the theory of partially hyperbolic systems [HPS] in order to find singularities of index 1 for vector fields with isolated zeroes in a 3 -ball. Indeed, we prove that such zeroes exists provided the maximal invariant set in the ball is partially hyperbolic, with volume expanding central subbundle, and the strong stable manifolds of the singularities are unknotted in the ball.

Hyperbolic homeomorphisms and bishadowing

P. E. Kloeden, J. Ombach (1997)

Annales Polonici Mathematici

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Hyperbolic homeomorphisms on compact manifolds are shown to have both inverse shadowing and bishadowing properties with respect to a class of δ-methods which are represented by continuous mappings from the manifold into the space of bi-infinite sequences in the manifold with the product topology. Topologically stable homeomorphisms and expanding mappings are also considered.