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Tangences homoclines stables pour des ensembles hyperboliques de grande dimension fractale

Carlos Gustavo Moreira, Jean-Christophe Yoccoz (2010)

Annales scientifiques de l'École Normale Supérieure

Soit F 0 un difféomorphisme d’une surface possédant deux fers à cheval Λ , Λ ' tels que W s Λ et W u Λ ' aient en un point q une tangence quadratique isolée. Nous montrons que, si la somme des dimensions transverses de W s Λ et W u Λ ' est strictement plus grande que 1, les difféomorphismes voisins de F 0 tels que W s Λ et W u Λ ' soient stablement tangents au voisinage de q forment une partie de densité inférieure strictement positive en F 0 .

The behaviour of the nonwandering set of a piecewise monotonic interval map under small perturbations

Peter Raith (1997)

Mathematica Bohemica

In this paper piecewise monotonic maps T [ 0 , 1 ] → [ 0 , 1 ] are considered. Let Q be a finite union of open intervals, and consider the set R ( Q ) of all points whose orbits omit Q . The influence of small perturbations of the endpoints of the intervals in Q on the dynamical system ( R ( Q ) , T ) is investigated. The decomposition of the nonwandering set into maximal topologically transitive subsets behaves very unstably. Nonetheless, it is shown that a maximal topologically transitive subset cannot be completely destroyed by arbitrary...

The Bernoulli shift as a basic chaotic dynamical system

Kučera, Václav (2019)

Programs and Algorithms of Numerical Mathematics

We give a brief introduction to the Bernoulli shift map as a basic chaotic dynamical system. We give several examples where the iterates of a~mapping can be understood using the Bernoulli shift. Namely, the iteration of real interval maps and iteration of quadratic functions in the complex plain.

The Conley index and countable decompositions of invariant sets

Marian Gidea (1999)

Banach Center Publications

We define a new cohomological index of Conley type associated to any bi-infinite sequence of neighborhoods that satisfies a certain isolation condition. We use this index to study the chaotic dynamics on invariant sets which decompose as countable unions of pairwise disjoint (mod 0) compact pieces.

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