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2000 | 143 | 2 | 103-119
Tytuł artykułu

The asymptotics of the Perron-Frobenius operator of a class of interval maps preserving infinite measures

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We determine the asymptotic behaviour of the iterates of the Perron-Frobenius operator for specific interval maps with an indifferent fixed point which gives rise to an infinite invariant measure.
Słowa kluczowe
Czasopismo
Rocznik
Tom
143
Numer
2
Strony
103-119
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-10-12
poprawiono
2000-10-09
Twórcy
  • Institute of Mathematics, University of Salzburg, Hellbrunnerstr. 34 , A-5020 Salzburg, Austria
Bibliografia
  • [A0] J. Aaronson, An Introduction to Infinite Ergodic Theory, Amer. Math. Soc., 1997.
  • [A1] J. Aaronson, The asymptotic distributional behaviour of transformations preserving infinite measures, J. Anal. Math. 39 (1981), 203-234.
  • [A2] J. Aaronson, Random f-expansions, Ann. Probab. 14 (1986), 1037-1057.
  • [BG] A. Boyarsky and P. Góra, Laws of Chaos. Invariant Measures and Dynamical Systems in One Dimension, Birkhäuser, 1997.
  • [Fe] W. Feller, An Introduction to Probability Theory and its Applications, Vol. II, Wiley, 1971.
  • [Fr] N. A. Friedman, Mixing transformations in an infinite measure space, in: Studies in Probability and Ergodic Theory, Adv. Math. Suppl. Stud. 2, Academic Press, 1978, 167-184.
  • [HK] A. B. Hajian and S. Kakutani, Weakly wandering sets and invariant measures, Trans. Amer. Math. Soc. 110 (1964), 136-151.
  • [H] E. Hopf, Ergodentheorie, Springer, 1937.
  • [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.
  • [LM] A. Lasota and M. C. Mackey, Chaos, Fractals, and Noise. Stochastic Aspects of Dynamics, Springer, 1994.
  • [Kr] K. Krickeberg, Strong mixing properties of Markov chains with infinite invariant measure, in: Proc. Fifth Berkeley Sympos. Math. Statist. Probab. 2, Part II, Univ. of California Press, 1965, 431-445.
  • [M] P. Manneville, Intermittency, self-similarity and 1/f spectrum in dissipative dynamical systems, J. Phys. 41 (1980), 1235-1243.
  • [P] F. Papangelou, Strong ratio limits, R-recurrence and mixing properties of discrete parameter Markov processes, Z. Wahrsch. Verw. Gebiete 8 (1967), 259-297.
  • [R] M. Rychlik, Bounded variation and invariant measures, Studia Math. 76 (1983), 69-80.
  • [Sch1] F. Schweiger, Invariant measures for piecewise linear fractional maps, J. Austral. Math. Soc. Ser. A 34 (1983), 55-59.
  • [Sch2] F. Schweiger, Ergodic Theory of Fibered Systems and Metric Number Theory, Clarendon Press, 1995.
  • [T1] M. Thaler, Estimates of the invariant densities of endomorphisms with indifferent fixed points, Israel J. Math. 37 (1980), 303-314.
  • [T2] M. Thaler, Transformations on [0,1] with infinite invariant measures, ibid. 46 (1983), 67-96.
  • [T3] M. Thaler, The iteration of the Perron-Frobenius operator when the invariant measure is infinite: An example, manuscript, Salzburg, 1986.
  • [T4] M. Thaler, Arc-sine limit laws for a one-parameter family of f-expansions, manuscript, Salzburg, 1993.
  • [T5] M. Thaler, A limit theorem for the Perron-Frobenius operator of transformations on [0,1] with indifferent fixed points, Israel J. Math. 91 (1995), 111-127.
  • [T6] M. Thaler, The invariant densities for maps modeling intermittency, J. Statist. Phys. 79 (1995), 739-741.
  • [T7] M. Thaler, The Dynkin-Lamperti arc-sine laws for measure preserving transformations, Trans. Amer. Math. Soc. 350 (1998), 4593-4607.
  • [TR] M. Thaler and C. Reichsöllner, Arc sine type limit laws for interval mappings, manuscript, Salzburg, 1986.
  • [Z1] R. Zweimüller, Ergodic structure and invariant densities of non-Markovian interval maps with indifferent fixed points, Nonlinearity 11 (1998), 1263-1276.
  • [Z2] R. Zweimüller, Ergodic properties of infinite measure-preserving interval maps with indifferent fixed points, Ergodic Theory Dynam. Systems 20 (2000), 1519-1549.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv143i2p103bwm
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