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Asymptotic windings over the trefoil knot.

Jacques Franchi (2005)

Revista Matemática Iberoamericana

Consider the group G:=PSL2(R) and its subgroups Γ:= PSL2(Z) and Γ':=DSL2(Z). G/Γ is a canonical realization (up to an homeomorphism) of the complement S3T of the trefoil knot T, and G/Γ' is a canonical realization of the 6-fold branched cyclic cover of S3T, which has a 3-dimensional cohomology of 1-forms.Putting natural left-invariant Riemannian metrics on G, it makes sense to ask which is the asymptotic homology performed by the Brownian motion in G/Γ', describing thereby in an intrinsic way part...

Attractors and Inverse Limits.

James Keesling (2008)

RACSAM

This paper surveys some recent results concerning inverse limits of tent maps. The survey concentrates on Ingram’s Conjecture. Some motivation is given for the study of such inverse limits.

Averaging method for differential equations perturbed by dynamical systems

Françoise Pène (2002)

ESAIM: Probability and Statistics

In this paper, we are interested in the asymptotical behavior of the error between the solution of a differential equation perturbed by a flow (or by a transformation) and the solution of the associated averaged differential equation. The main part of this redaction is devoted to the ascertainment of results of convergence in distribution analogous to those obtained in [10] and [11]. As in [11], we shall use a representation by a suspension flow over a dynamical system. Here, we make an assumption...

Averaging method for differential equations perturbed by dynamical systems

Françoise Pène (2010)

ESAIM: Probability and Statistics

In this paper, we are interested in the asymptotical behavior of the error between the solution of a differential equation perturbed by a flow (or by a transformation) and the solution of the associated averaged differential equation. The main part of this redaction is devoted to the ascertainment of results of convergence in distribution analogous to those obtained in [10] and [11]. As in [11], we shall use a representation by a suspension flow over a dynamical system. Here, we make an assumption...

Axiom A versus Newhouse phenomena for Benedicks-Carleson toy models

Carlos Matheus, Carlos G. Moreira, Enrique R. Pujals (2013)

Annales scientifiques de l'École Normale Supérieure

We consider a family of planar systems introduced in 1991 by Benedicks and Carleson as a toy model for the dynamics of the so-called Hénon maps. We show that Smale’s Axiom A property is C 1 -dense among the systems in this family, despite the existence of  C 2 -open subsets (closely related to the so-called Newhouse phenomena) where Smale’s Axiom A is violated. In particular, this provides some evidence towards Smale’s conjecture that Axiom A is a C 1 -dense property among surface diffeomorphisms. The basic...

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