Exponential decay of correlations for randomly chosen hyperbolic toral automorphisms.
نویسندگان
چکیده
We consider pairs of toral automorphisms (A,B) satisfying an invariant cone property. At each iteration, A acts with probability p is in (0,1) and B with probability 1-p. We prove exponential decay of correlations for a class of Hölder continuous observables.
منابع مشابه
Controlling Strong Scarring for Quantized Ergodic Toral Automorphisms
We show that in the semiclassical limit the eigenfunctions of quantized ergodic symplectic toral automorphisms cannot concentrate in measure on closed orbits of the dynamics. More generally, we show that the mass of the pure point component of the limit measure must be smaller than two thirds of the total mass. The proofs use only the algebraic (i.e., not the number-theoretic) properties of the...
متن کاملRapid Decay of Correlations for Nonuniformly Hyperbolic Flows
We show that superpolynomial decay of correlations (rapid mixing) is prevalent for a class of nonuniformly hyperbolic flows. These flows are the continuous time analogue of the class of nonuniformly hyperbolic maps for which Young proved exponential decay of correlations. The proof combines techniques of Dolgopyat and operator renewal theory. It follows from our results that planar periodic Lor...
متن کاملToral Automorphisms and Applications to Norm-euclidean Domains and Euclidean Minima
A number field modulo its ring of integers is a torus, and the units act on this torus as hyperbolic toral automorphisms. We show sufficient control over the distribution of the rational orbits to give a new, non-computational proof that Q( √ 2 + √ 2) is a normEuclidean number field, and an improved upper bound for the Euclidean minima of real cyclotomic fields of power of 2 conductor.
متن کاملMarkov Partitions and Homoclinic Pointsof
We prove that a general class of expansive Z d-actions by automorphisms of compact, abelian groups with completely positive en-tropy has`symbolic covers' of equal topological entropy. These symbolic covers are constructed by using homoclinic points of these actions. For d = 1 we adapt a result of Kenyon and Vershik in 7] to prove that these symbolic covers are, in fact, sooc shifts. For d 2 we ...
متن کاملChaos, Quantization and the Classical Limit on the Torus
The algebraic and the canonical approaches to the quantization of a class of classical symplectic dynamical systems on the two-torus are presented in a simple unified framework. This allows for ready comparison between the two very different approaches and is well adapted to the study of the semi-classical behaviour of the resulting models. Ergodic translations and skew translations, as well as...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Chaos
دوره 17 4 شماره
صفحات -
تاریخ انتشار 2007