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Local complexity growth for iterations of real analytic mappings and semicontinuity moduli of the entropy

Published online by Cambridge University Press:  19 September 2008

Y. Yomdin
Affiliation:
The Weizmann Institute of Science, Rehovot 76100, Israel

Abstract

We consider some ways in which regularity of a mapping influences dynamics of its iterations and growth of various complexity-type invariants.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1991

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References

REFERENCES

[1]Arnold, V.. CUNY talk, 10 1988.Google Scholar
[2]Bernstein, S.. Sur l'ordre de la meilleure approximation des functions continues par des polynomies de degré donné. Memoires Publiés par la Classe des sc. Acad. de Belgique, 2, vol. 4 (1912), 1103.Google Scholar
[3]Friedland, S.. Entropy of polynomial and rational maps. Preprint (1988).Google Scholar
[4]Friedland, S. & Milnor, J.. Dynamical properties of plane polynomial automorphisms. Preprint (1987).Google Scholar
[5]Gromov, M.. On the entropy of holomorphic maps. Preprint (1977).Google Scholar
[6]Gromov, M.. Entropy, homology and semialgebraic geometry (after Y. Yomdin). Seminaire N. Bourbaki (19851986), no. 663.Google Scholar
[7]Katok, A.. Lyapunov exponents, entropy and periodic orbits for diffeomorphisms. Publ. Math. IHES 51 (1980), 137173.CrossRefGoogle Scholar
[8]Knieper, G. & Wein, H.. To appear.Google Scholar
[9]Milnor, J.. Non-expansive Hénon maps. Preprint (1987).Google Scholar
[10]Misiurewicz, M.. On non-continuity of topological entropy. Bull, de L'Acad. Polonaise des Sci. XIX (4) (1971), 319320.Google Scholar
[11]Misiurewicz, M.. Diffeomorphisms without any measure with maximal entropy. Bull, de l'Acad. Polonaise des Sci. XXI (10) (1973), 903910.Google Scholar
[12]Newhouse, S.. Ergod. Th. & Dynam. Sys. 8* (1988), 283299.Google Scholar
[13]Newhouse, S.. Continuity properties of entropy. To appear.Google Scholar
[14]Newhouse, S.. Personal communication.Google Scholar
[15]Teissier, B.. Sur trois questions de finitude en géométrie analytique reelle. Appendix to the paper F. Treves, On the local solvability and local integrability of systems of vector fields. Acta Math. 151 (1983), 248.Google Scholar
[16]Yomdin, Y.. Volume growth and entropy. Israel J. Math. 57 (3) (1987), 285300.CrossRefGoogle Scholar
[17]Yomdin, Y.. Ck-resolution of semialgebraic mappings. Israel J. Math. 57 (3) (1987), 301317.CrossRefGoogle Scholar
[18]Yomdin, Y.. Approximative complexity of functions. In: Geometric Aspects of Functional Analysis. Lindenstrauss, J., Milman, V. D., eds, Springer Lecture Notes in Mathematics 1317 (1988), 2143.CrossRefGoogle Scholar
[19]Yomdin, Y.. Nonautonomous linearization. In: Dynamical Systems, ed Alexander, J. C.. Springer Lecture Notes in Mathematics 1342 (1988), pp. 718726.CrossRefGoogle Scholar
[20]Ziemian, K.. Rate of convergence of conditional entropies for some maps of an interval. Preprint (1987).Google Scholar