Abstract
It is an important problem in the theory of concrete dissipative dynamical systems to construct the relevant invariant measure. A rather complete theory has been developed for the case of uniformly hyperbolic dynamical systems following the initial ideas of Sinaï Bowen and Ruelle. They proved an equivalence between questions about invariant measures and problems in statistical mechanics. In particular, the interesting invariant measures are Gibbs states of a one dimensional spin system.
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References
J. Aaronson. Journal d’Analyse Mathematique 39, 203 (1981).
R. Bowen. Commun. Math. Phys. 69, 1 (1979).
P.Collet, P.Ferrero. To appear.
W.F. Donoghue. Monotone Matrix Functions and Analytic Continuation. Springer Verlag, Berlin Heidelberg New York 1974.
U. Krengel. Ergodic Theorems. De Gruyter Studies in Mathematics 6, Walter de Gruyter, Berlin New York 1985.
P. Manneville. Journal de Physique 41, 1235 (1980).
C. Meunier. Journ. Stat. Phys. 36, 3 (1984).
M. Thaler. Isr. Journ. Math. 37, 303 (1980).
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© 1989 Kluwer Academic Publishers
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Collet, P., Ferrero, P. (1989). Absolutely Continuous Invariant Measure for Expanding Pick Maps of the Interval Except at a Marginal Fixed Point. In: Tirapegui, E., Villarroel, D. (eds) Instabilities and Nonequilibrium Structures II. Mathematics and Its Applications, vol 50. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2305-8_2
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DOI: https://doi.org/10.1007/978-94-009-2305-8_2
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