Powiadomienia systemowe
- Sesja wygasła!
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
There are introduced the concepts of deterministic, exact and Kolmogorov flows which are topological analogues of the well known measure-theoretic dynamical systems with the same names. It is shown that all distal flows are deterministic and that the only deterministic subshifts are those with a finite phase space. Deterministic flows have zero entropy. The class of Kolmogorov flows contains flows acting on zero-dimensional phase spaces being measure-theoretic Kolmogorov systems with respect to measures with full supports. All minimal Kolmogorov flows are weakly mixing.
Wydawca
Rocznik
Tom
Strony
401--417
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
autor
- Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
autor
- Faculty of Mathematics and Computer Science, University of Warmia and Mazury, Żołnierska 14A, 10-631 Olsztyn, Poland
autor
- Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
Bibliografia
- [1] J. Auslander, Minimal flows and their extensions, Elseviers Science Publishers B.V., 1988.
- [2] F. Blanchard, Fully positive topological entropy and topological mixing, Contemp. Math., 135 (1992) 95-105.
- [3] F. Blanchard, B. Host, S. Ruette, Asymptotic pairs in positive-entropy systems, Ergodic. Theory Dynam. Systems, 22 (2002) 671-686.
- [4] M. Denker, C. Grillenberger, K. Sigmund, Ergodic theory on compact spaces, Lecture Notes in Math., 527, Springer-Verlag, Berlin Heidelberg New York 1976.
- [5] M. Denker, M. Urbański, Ergodic theory of equilibrium states for rational maps, Nonlinearity, 4 (1991) 103-134.
- [6] R. Ellis, Lectures on topological dynamics, W. A. Benjamin, Inc., New York 1969.
- [7] H. Furstenberg, Strict ergodicity and transformations of the torus, Amer. J. Math., 83 (1961) 573-601.
- [8] H. Furstenberg, Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation, Math. Syst. Th., 1 (1967) 1-49.
- [9] W. Geller, M. Misiurewicz, Rotation and entropy, Trans. Amer. Math. Soc., 251 (1999) 2927-2948.
- [10] S. Glasner, D. Maon, Rigidity in topological dynamics, Ergodic Theory Dynam. Systems, 9 (1989) 309-320.
- [11] K. Krzyżewski, On exact toral endomorphisms, Monatsh. Math., 116 (1993) 39-47.
- [12] R. Mañé, Expansive homeomorphisms and topological dimension, Trans. Amer. Math. Soc., 252 (1979) 313-319.
- [13] W. Parry, Symbolic dynamics and transformations of the unit interval, Trans. Amer. Math. Soc., 122 (1966) 168-178.
- [14] V. A. Rokhlin, On the fundamental ideas of measure theory (Russian), Mat. Sb., 25 (1949) 107-150.
- [15] V. A. Rokhlin, Exact endomorphisms of a Lebesgue space (Russian), Izv. Akad. Nauk, 22 (1967) 499-530.
- [16] V. A. Rokhlin, Lectures on the entropy theory of transformations with invariant measure (Russian), Uspekhi Mat. Nauk, 22 (5) (1967) 3-56.
- [17] V. A. Rokhlin, Y. G. Sinai, Construction and properties of invariant measurable partitions (Russian), Dokl. Akad. Nauk SSSR, 141 (1961) 1038-1041.
- [18] A. Siemaszko, J. Szymański, On exact topological flows, Topol. Methods Nonlinear Anal., 21 (2003) 387-392.
- [19] P. Walters, An introduction to Ergodic Theory, Springer-Verlag, New York, Heidelberg, Berlin 1982.
- [20] B. Weiss, Multiple recurrence and doubly minimal systems, Contemp. Math., 215 (1998) 189-196.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0001-0079