The entropy of polynomial diffeomorphisms of \({\mathbb{C}}^ 2\). (English) Zbl 0695.58023

This paper contains a calculation of the entropy of polynomial diffeomorphisms of \({\mathbb{C}}^ 2\). This calculation answers a question raised by S. Friedland and J. Milnor in Ergodic Theory Dyn. Syst. 9, No.1, 67-99 (1989; Zbl 0651.58027). The proof relies on the result of Yomdin which shows that the growth rate for volume is a lower bound for entropy.
Reviewer: J.Smillie


37D99 Dynamical systems with hyperbolic behavior
37A99 Ergodic theory
32H50 Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables
Full Text: DOI


[1] DOI: 10.1007/BF02766215 · Zbl 0641.54036
[2] Gromov, Seminaire N. Bourbaki 663 pp none– (1985)
[3] Bowen, Proc. Symp. Pure Math. 14 pp 23– (1970)
[4] DOI: 10.1007/BF01221362 · Zbl 0414.58028
[5] Friedland, Ergod. Th. & Dynam. Sys. 9 pp 67– (1989)
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