Ergodic Dynamical Systems Conjugate to Their Composition Squares
نویسنده
چکیده
We investigate the question of when an ergodic automorphism T is conjugate to its composition square T 2, i.e., when does there exist an automorphism S with the property that ST = T 2S. This is a non–generic property of automorphisms which seems to be quite exceptional. The situation for ergodic automorphisms having discrete spectrum and automorphisms having the weak closure property is investigated.
منابع مشابه
SOME ERGODIC PROPERTIES OF HYPER MV {ALGEBRA DYNAMICAL SYSTEMS
This paper provides a review on major ergodic features of semi-independent hyper MV {algebra dynamical systems. Theorems are presentedto make contribution to calculate the entropy. Particularly, it is proved that thetotal entropy of those semi-independent hyper MV {algebra dynamical systemsthat have a generator can be calculated with respect to their generator ratherthan considering all the par...
متن کاملRELATIVE INFORMATION FUNCTIONAL OF RELATIVE DYNAMICAL SYSTEMS
In this paper by use of mathematical modeling of an observer [14,15] the notion of relative information functional for relative dynamical systemson compact metric spaces is presented. We extract the information function ofan ergodic dynamical system (X,T) from the relative information of T fromthe view point of observer χX, where X denotes the base space of the system.We also generalize the in...
متن کاملTopological Classiication of Linear Hyperbolic Cocycles
In this paper linear hyperbolic cocycles are classiied by the relation of topological conjugacy. Roughly speaking, two linear cocycles are conjugate if there exists a homeomorphism which maps their tra-jectories into each other. The problem of classiication of discrete-time deterministic hyperbolic dynamical systems was investigated by Rob-bin (1972). He proved that there exist 4d classes of d-...
متن کاملSmooth Ergodic Theory and Nonuniformly Hyperbolic Dynamics
Introduction 1 1. Lyapunov exponents of dynamical systems 3 2. Examples of systems with nonzero exponents 6 3. Lyapunov exponents associated with sequences of matrices 18 4. Cocycles and Lyapunov exponents 24 5. Regularity and Multiplicative Ergodic Theorem 31 6. Cocycles over smooth dynamical systems 46 7. Methods for estimating exponents 54 8. Local manifold theory 62 9. Global manifold theor...
متن کاملOn Strong Ergodic Properties of Quantum Dynamical Systems
Abstract. We show that the the shift on the reduced C∗–algebras of RD–groups, including the free group on infinitely many generators, and the amalgamated free product C∗–algebras, enjoys the very strong ergodic property of the convergence to the equilibrium. Namely, the free shift converges, pointwise in the weak topology, to the conditional expectation onto the fixed–point subalgebra. Provided...
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:
دوره شماره
صفحات -
تاریخ انتشار 2003