Abstract
The study of the general structure of dynamical systems, begun in the previous sections, could continue and constitutes one of the directions in which ergodic theory can be developed. We shall, however, look in a somewhat different direction dedicating attention to a few concrete problems that do not belong to the general theory. The more concrete studies involve analytic work of “classical” type and are more directly related to the applications.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Bibliographical Note to Sect. 5.4
Renij, A.: Representations for real numbers and their ergodic properties, Acta Mathematica, Academia Scientiae Hungarica 8 (1957), 477–493.
Ulam, S., Von Neumann, J.: On combination of stochastic and deterministic processes, Bulletin of the American Mathematical Society 53 (1947), 1120.
Lasota, A., Yorke, J.: On the existence of invariant measures for a piecewise monotonic transformation, Transactions of the American Mathematical Society 186 (1973), 481–488.
Lanford, O.: Qualitative and statistical theory of dissipative systems, Statistical Mechanics, C.I.M.E., I° ciclo (1976), pp. 25–98, Liguori, Naples, 1978.
Ruelle, D.: Application conservant une mesure absolument continue par rapport a dx sur [0, 1], Communications in Mathematical Physics 55 (1977), 47–51.
Bowen, R.: Equilibrium states and the ergodic theory of Anosov diffeormorphisms, Lecture Notes in Mathematics, Vol. 470, Springer-Verlag, Berlin-Heidelberg, 1975.
Collet, F., Eckmann, J.-P.: Iterated maps of the interval, Birkhauser, Boston, 1980.
Pianigiani, G.: Absolutely continuous invariant measures for the process x n+1 = Ax n (1 − x n ), Bollettino dell’Unione Matematica Italiana A 16 (1979), no. 2, 374–378.
Pianigiani, G.: First return map and invariant measures, Israel Journal of Mathematics 35 (1980), no. 1–2, 32–48.
Pianigiani, G.: Existence of invariant measures for piecewise continous transformations, Annales Polonici Mathematici 40 (1981), no. 1, 39–45.
Pianigiani, G., Yorke, J.: Exanding maps on sets which are almost invari-ant: decay and chaos (dedicated to J. Massera), Transactions of the American Mathematical Society 252 (1979), 351–366.
Feigenbaum, M.: Quantitative universality for a class of nonlinear transformations, Journal of Statistical Physics 19 (1978), no. 1, 25–52.
Feigenbaum, M.: The universal metric properties of nonlinear transformations, Journal of Statistical Physics 21 (1979), no. 6, 669–706.
Collet, P., Eckmann, J.-P., Lanford, O.: Universal properties of maps on an Interval, Communications in Mathematical Physics 76 (1980), 211–254.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Gallavotti, G., Bonetto, F., Gentile, G. (2004). Gibbs Distributions. In: Aspects of Ergodic, Qualitative and Statistical Theory of Motion. Texts and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05853-4_5
Download citation
DOI: https://doi.org/10.1007/978-3-662-05853-4_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07416-5
Online ISBN: 978-3-662-05853-4
eBook Packages: Springer Book Archive