Metric attractors for smooth unimodal maps
نویسندگان
چکیده
منابع مشابه
Metric attractors for smooth unimodal maps
We classify the measure theoretic attractors of general C 3 unimodal maps with quadratic critical points. The main ingredient is the decay of geometry.
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 کاملSmooth Deformations of Piecewise Expanding Unimodal Maps
In the space of C piecewise expanding unimodal maps, k ≥ 2, we characterize the C smooth families of maps where the topological dynamics does not change (the “smooth deformations”) as the families tangent to a continuous distribution of codimension-one subspaces (the “horizontal” directions) in that space. Furthermore such codimension-one subspaces are defined as the kernels of an explicit clas...
متن کاملBifurcations of Chaotic Attractors in One-Dimensional Piecewise Smooth Maps
It is well known that dynamical systems defined by piecewise smooth functions exhibit several phenomena which cannot occur in smooth systems, such as for example, border collision bifurcations, sliding, chattering, etc. [di Bernardo et al., 2008]. One such phenomenon is the persistence of chaotic attractors under parameter perturbations, referred to as robust chaos [Banerjee et al., 1998]. In t...
متن کاملBifurcations of Unimodal Maps
We review recent results that lead to a very precise understanding of the dynamics of typical unimodal maps from the statistical point of view. We also describe the (generalized) renormalization approach to the study of the statistical properties of typical unimodal maps.
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: Annals of Mathematics
سال: 2004
ISSN: 0003-486X
DOI: 10.4007/annals.2004.159.725