Abstract
We study the topological entropy h of an one parameter endomorphism ψ of the unit interval, when its extremum trajectory is periodic. Some families of recurrent polynomials show the “local” behaviour of h, especially in the neighbourhood of the fixed point of ψ.
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.
References
J. COUOT. “Invariant Measures and Topological Entropy of Complex Stationary States of Dynamic Systems...” Proceedings of the VIIIth ICNO, 1978, Prague, p. 205–210.
J. COUOT, C. GILLOT, G. GILLOT. “Détermination Numérique des Densités de Suites Récurrentes”. Comportement des Processus Itératifs, 1979, La Garde Freinet.
J. COUOT, C. GILLOT, G. GILLOT. “Quelques Simulations Numériques de Densités de Suites Récurrentes”. Publications du Groupe “Systèmes Dynamiques non Linéaires”, 1979.
M. DENKER, C. GRILLENBERGER, K. SIGMUND. “Ergodic Theory on Compact Spaces”, Lecture Notes in Mathematics, Vol. 527 (Springer Berlin, Heidelberg, New York 1976)
F.R. GANTMACHER. “Théorie des Matrices”. Dunod, 1966, Paris.
J. GUCKENHEIMER. “Sensitive Dependance to Initial Conditions for One Dimensional Maps”. Publications I.H.E.S., 1979.
L. JONKER. “Periodic Orbits and Kneading Invariants”. Proc. London. Math. Soc (3) 1979, p. 428–450.
I. MILNOR, W. THURSTON. “On Iterated Maps of the Interval. The Kneading Matrix”. Preprint.
C. MIRA. “Dynamique Complexe engendrée par une Récurrence, ou Transformation Ponctuelle, Continue, Linéaire par Morceaux”. C.R. Acad. Sci. Paris (285) 1977, p. 731–734.
M. MISIUREWICZ, W. SLENK. “Entropy of Piecewise Monotone Mappings”. Asterisque, Soc. Math. de France (50), 1977.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1981 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gillot, C., Gillot, G. (1981). Topological Entropy of Markov Processes for a C0- Endomorphism of the Interval. In: Della Dora, J., Demongeot, J., Lacolle, B. (eds) Numerical Methods in the Study of Critical Phenomena. Springer Series in Synergetics, vol 9. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81703-8_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-81703-8_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-81705-2
Online ISBN: 978-3-642-81703-8
eBook Packages: Springer Book Archive