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1998 | 69 | 1 | 13-24
Tytuł artykułu

Invariant measures and the compactness of the domain

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider piecewise monotonic and expanding transformations τ of a real interval (not necessarily bounded) into itself with countable number of points of discontinuity of τ' and with some conditions on the variation $V_{[0,x]}(1/|τ'|)$ which need not be a bounded function (although it is bounded on any compact interval). We prove that such transformations have absolutely continuous invariant measures. This result generalizes all previous "bounded variation" existence theorems.
Słowa kluczowe
Rocznik
Tom
69
Numer
1
Strony
13-24
Opis fizyczny
Daty
wydano
1998
otrzymano
1995-10-20
poprawiono
1997-09-29
Twórcy
  • Institute of Computer Science, Jagiellonian University, Nawojki 11, 30-072 Kraków, Poland
autor
  • 7141 Sherbrooke Street West, Montreal, Quebec, Canada H4B 1R6
Bibliografia
  • [Gó] P. Góra, Properties of invariant measures for piecewise expanding transformations with summable oscillation of the derivative, Ergodic Theory Dynam. Systems 14 (1994), 475-492.
  • [JGB] M. Jabłoński, P. Góra and A. Boyarsky, A general existence theorem for absolutely continuous invariant measures on bounded and unbounded intervals, Nonlinear World 2 (1995), 183-200.
  • [JL] M. Jabłoński and A. Lasota, Absolutely continuous invariant measures for transformations on the real line, Zeszyty Nauk. Uniw. Jagiell. Prace Mat. 22 (1981), 7-13.
  • [KS] A. A. Kosyakin and E. A. Sandler, Ergodic properties of a certain class of piecewise smooth transformations of a segment, Izv. Vyssh. Uchebn. Zaved. Mat. 1972, no. 3, 32-40 (in Russian).
  • [LY] A. Lasota and J. A. Yorke, On the existence of invariant measures for piecewise monotonic transformations, Trans. Amer. Math. Soc. 186 (1973), 481-488.
  • [Re] A. Rényi, Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hungar. 8 (1957), 477-493.
  • [Ry] M. R. Rychlik, Bounded variation and invariant measures, Studia Math. 76 (1983), 69-80.
  • [Sch] B. Schmitt, Contributions à l'étude de systèmes dynamiques unidimensionnels en théorie ergodique, Ph.D. Thesis, University of Bourgogne, 1986.
  • [Wo] S. Wong, Some metric properties of piecewise monotonic mappings of the unit interval, Trans. Amer. Math. Soc. 246 (1978), 493-500.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv69z1p13bwm
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