A nondifferentiable essential irrational invariant curve for a $C^1$ symplectic twist map

A non-differentiable essential irrational invariant curve for a C symplectic twist map

We construct a C1 symplectic twist map f of the annulus that has an essential invariant curve Γ such that: • Γ is not differentiable; • the dynamic of f|Γ is conjugated to the one of a Denjoy counter-example. ANR KAM faible ANR-07-BLAN-0361 ANR DynNonHyp ANR BLAN08-2-313375 Université d’Avignon et des Pays de Vaucluse, Laboratoire d’Analyse non linéaire et Géométrie (EA 2151), F-84 018Avignon, ...

A C1 Map with Invariant Cantor Set of Positive Measure

Many examples exist of one-dimensional systems that are topologically conjugate to the shift operator on Σ2 and are thus chaotic. Most of these examples which have invariant Cantor subsets, have Cantor subsets of measure zero. In this paper we outline the formulation of a C map on a closed interval that has an invariant Cantor subset of positive Lebesgue measure. We also survey techniques used ...

Modeling the Invariant Density Curve of a Noisy Chaotic Map

The goal of the research is to analytically determine the invariant density curve for a given chaotic map altered by noise and to compare it to a numerically generated invariant density curve for the same map. The existence of an analytic solution allows one to predict the overall behavioral trend, if not the exact orbit, of a map and is potentially tremendously useful in the modeling of any sy...

Packing stability for irrational symplectic 4-manifolds

The packing stability in symplectic geometry was first noticed by Biran [Bir97]: the symplectic obstructions to embed several balls into a manifold disappear when their size is small enough. This phenomenon is known to hold for all closed manifolds with rational symplectic class (see [Bir99] for the 4-dimensional case, and [BH11, BH13] for higher dimensions), as well as ellipsoids [BH13]. In th...

Symplectic Twist Maps