Soit un difféomorphisme d’une surface possédant deux fers à cheval tels que et aient en un point une tangence quadratique isolée. Nous montrons que, si la somme des dimensions transverses de et est strictement plus grande que 1, les difféomorphismes voisins de tels que et soient stablement tangents au voisinage de forment une partie de densité inférieure strictement positive en .
In this paper piecewise monotonic maps are considered. Let be a finite union of open intervals, and consider the set of all points whose orbits omit . The influence of small perturbations of the endpoints of the intervals in on the dynamical system 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...
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.
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.