## 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

### Keywords:

entropy of polynomial diffeomorphisms

### Citations:

Zbl 0665.58031; Zbl 0651.58027
Full Text:

### 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)
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