Polynomial diffeomorphisms of ². II. Stable manifolds and recurrence
作者： Eric Bedford , John Smillie
DOI: 10.1090/S0894-0347-1991-1115786-3
关键词:
摘要: f(x,y)= (y,y ax +c). The diffeomorphisms in this class have complicated dynamics: particular, they periodic points of infinitely many periods and positive topological entropy (see [FM, S]). We can distinguish between these classes by considering the growth degrees iterates diffeomorphism. Define deg(f ) to be maximum coordinate functions. This quantity is not a conjugacy invariant f, hence dynamical invariant. construct invariant, which we call degree, as follows:
ams.org
jstor.org 
sci-hub.se 参考文章(10)
Curt McMullen, Ben Bielefeld, Jack Milnor, Folkert Tangerman, Adrien Douady, Peter Veerman, Misuhiro Shishikura, Conformal dynamics problem list arXiv: Dynamical Systems. ,(1990)
Jean-Pierre Rosay, Walter Rudin, Holomorphic maps from ⁿ to ⁿ Transactions of the American Mathematical Society. ,vol. 310, pp. 47- 86 ,(1988) , 10.1090/S0002-9947-1988-0929658-4
Eric Bedford, On the automorphism group of a stein manifold Mathematische Annalen. ,vol. 266, pp. 215- 227 ,(1983) , 10.1007/BF01458443
Eric Bedford, John Smillie, Polynomial diffeomorphisms of C2: currents, equilibrium measure and hyperbolicity. Inventiones Mathematicae. ,vol. 103, pp. 69- 99 ,(1991) , 10.1007/BF01239509
Jean-Pierre Rosay, Walter Rudin, Holomorphic Maps from C n to C n Transactions of the American Mathematical Society. ,vol. 310, pp. 47- ,(1988) , 10.2307/2001110
John Smillie, The entropy of polynomial diffeomorphisms of C2 Ergodic Theory and Dynamical Systems. ,vol. 10, pp. 823- 827 ,(1990) , 10.1017/S0143385700005927
David E. Barrett, Eric Bedford, Jiri Dadok, T n -actions on holomorphically separable complex manifolds Mathematische Zeitschrift. ,vol. 202, pp. 65- 82 ,(1989) , 10.1007/BF01180684
Shmuel Friedland, John Milnor, Dynamical properties of plane polynomial automorphisms Ergodic Theory and Dynamical Systems. ,vol. 9, pp. 67- 99 ,(1989) , 10.1017/S014338570000482X
Lars Hörmander, An introduction to complex analysis in several variables ,(1973)
Eduward Zehnder, A simple proof of a generalization of a theorem by C. L. Siegel Lecture Notes in Mathematics. pp. 855- 866 ,(1977) , 10.1007/BFB0085385