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Sulla stabilità di un punto fisso per funzioni di n variabili complesse. Problema del Centro di Schröder-Siegel

Timoteo Carletti (2005)

Bollettino dell'Unione Matematica Italiana

Viene considerato il problema della stabilità di un punto fisso per un germe di diffeomorfismo di più variabili complesse cercando un coniugio con la sua parte lineare: Problema del centro di Schröder-Siegel. Dopo aver formulato il problema e ricordato i principali risultati nel caso di diffeomorfismi olomorfi, mostriamo come estendere il problema ad alcune situazioni non olomorfe, in particolare ci interesseremo al caso di germi Gevrey. Concluderemo con un'applicazione rivolta a mostrare la stabilità...

S-unimodal Misiurewicz maps with flat critical points

Roland Zweimüller (2004)

Fundamenta Mathematicae

We consider S-unimodal Misiurewicz maps T with a flat critical point c and show that they exhibit ergodic properties analogous to those of interval maps with indifferent fixed (or periodic) points. Specifically, there is a conservative ergodic absolutely continuous σ-finite invariant measure μ, exact up to finite rotations, and in the infinite measure case the system is pointwise dual ergodic with many uniform and Darling-Kac sets. Determining the order of return distributions to suitable reference...

Sur les homéomorphismes du cercle de classe P C r par morceaux ( r ≥ 1 ) qui sont conjugués C r par morceaux aux rotations irrationnelles

Abdelhamid Adouani, Habib Marzougui (2008)

Annales de l’institut Fourier

Soit r ≥ 1 un réel. Ici, on étudie les homéomorphismes du cercle qui sont de classe P C r par morceaux et de nombres de rotation irrationnels. On caractérise ceux qui sont C r par morceaux conjugués à des C r -difféomorphismes. Comme conséquence, on obtient un critère de conjugaison...

Symbolic dynamics and Lyapunov exponents for Lozi maps

Diogo Baptista, Ricardo Severino (2012)

ESAIM: Proceedings

Building on the kneading theory for Lozi maps introduced by Yutaka Ishii, in 1997, we introduce a symbolic method to compute its largest Lyapunov exponent. We use this method to study the behavior of the largest Lyapunov exponent for the set of points whose forward and backward orbits remain bounded, and find the maximum value that the largest Lyapunov exponent can assume.

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 chain recurrent set for maps of compacta

Katsuya Yokoi (2007)

Annales Polonici Mathematici

For a self-map of a compactum we give a necessary and sufficient condition for the chain recurrent set to be precisely the set of periodic points.

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