Weakly hyperbolic invariant tori for two dimensional quasiperiodically forced maps in a degenerate case
نویسندگان
چکیده
منابع مشابه
Invariant measures for quasiperiodically forced circle homeomorphisms
We study quasiperiodically forced circle homeomorphisms and derive a basic classification with respect to the invariant ergodic measures for such systems: Either there exists an invariant graph and every invariant ergodic measure is associated to some invariant graph, or the system is uniquely ergodic. This immediately verifies an observation which is well-known from numerical studies, namely t...
متن کاملAttractors for Unimodal Quasiperiodically Forced Maps
We consider unimodal quasiperiodically forced maps, that is, skew products with irrational rotations of the circle in the base and unimodal interval maps in the fibers: the map in the fiber over θ is a unimodal map f of the interval [0, 1] onto itself multiplied by g(θ), where g is a continuous function from the circle to [0, 1]. Here we consider the “pinched” case, when g attains the value 0. ...
متن کاملCritical point of tori collision in quasiperiodically forced systems
We report on a type of scaling behavior in quasiperiodically forced systems. On the parameter plane the critical point appears as a terminal point of the tori-collision bifurcation curve; its location is found numerically with high precision for two basic models, the forced supercritical circle map and the forced quadratic map. The hypothesis of universality, based on renormalization group argu...
متن کاملHyperbolic low-dimensional invariant tori and summations of divergent series
Abstract. We consider a class of a priori stable quasi-integrable analytic Hamiltonian systems and study the regularity of low-dimensional hyperbolic invariant tori as functions of the perturbation parameter. We show that, under natural nonresonance conditions, such tori exist and can be identified through the maxima or minima of a suitable potential. They are analytic inside a disc centered at...
متن کاملExistence of invariant tori in three dimensional maps with degeneracy
We prove a KAM-type result for the persistence of two-dimensional invariant tori in perturbations of integrable action-angle-angle maps with degeneracy, satisfying the intersection property. Such degenerate action-angleangle maps arise upon generic perturbation of three-dimensional volumepreserving vector fields, which are invariant under volume-preserving action of S1 when there is no motion i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems
سال: 2016
ISSN: 1078-0947
DOI: 10.3934/dcds.2016086