Spectra of ergodic transformations
نویسندگان
چکیده
منابع مشابه
Ergodic Theory: Nonsingular Transformations
Glossary 1 1. Definition of the subject and its importance 2 2. Basic Results 2 3. Panorama of Examples 8 4. Mixing notions and multiple recurrence 10 5. Topological group Aut(X,μ) 13 6. Orbit theory 15 7. Smooth nonsingular transformations 21 8. Spectral theory for nonsingular systems 22 9. Entropy and other invariants 25 10. Nonsingular Joinings and Factors 27 11. Applications. Connections wi...
متن کاملConvergence of Multiple Ergodic Averages for Some Commuting Transformations
We prove the L convergence for the linear multiple ergodic averages of commuting transformations T1, . . . , Tl, assuming that each map Ti and each pair TiT −1 j is ergodic for i 6= j. The limiting behavior of such averages is controlled by a particular factor, which is an inverse limit of nilsystems. As a corollary we show that the limiting behavior of linear multiple ergodic averages is the s...
متن کاملErgodic and Spectral Analysis of Certain Infinite Measure Preserving Transformations
0. Introduction. Throughout this paper T will denote a measure preserving transformation on a cr-finite infinite measure space (X, (B, m) which is point isomorphic with the Lebesgue measure space of the real line. Unless otherwise stated, T will be one-one. Equations involving functions or sets will always be interpreted modulo sets of measure zero. T is said to be ergodic if T~1E = E, ££(B, im...
متن کاملNorm Convergence of Multiple Ergodic Averages for Commuting Transformations
Let T1, . . . , Tl : X → X be commuting measure-preserving transformations on a probability space (X,X , μ). We show that the multiple ergodic averages 1 N PN−1 n=0 f1(T n 1 x) . . . fl(T n l x) are convergent in L2(X,X , μ) as N → ∞ for all f1, . . . , fl ∈ L (X,X , μ); this was previously established for l = 2 by Conze and Lesigne [2] and for general l assuming some additional ergodicity hypo...
متن کاملErgodic Transformations in the Space of p-adic Integers
Let L1 be the set of all mappings f : Zp → Zp of the space of all p-adic integers Zp into itself that satisfy Lipschitz condition with a constant 1. We prove that the mapping f ∈L1 is ergodic with respect to the normalized Haar measure on Zp if and only if f induces a single cycle permutation on each residue ring Z/pZ modulo p, for all k = 1,2,3, . . .. The multivariate case, as well as measure...
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: Journal of Functional Analysis
سال: 1974
ISSN: 0022-1236
DOI: 10.1016/0022-1236(74)90019-6