×

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

MSC:

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
PDF BibTeX XML Cite
Full Text: DOI

References:

[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)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.