Author:
Arosio Leandro,Benini Anna Miriam,Fornæss John Erik,Peters Han
Abstract
<p style='text-indent:20px;'>Very little is currently known about the dynamics of non-polynomial entire maps in several complex variables. The family of transcendental Hénon maps offers the potential of combining ideas from transcendental dynamics in one variable and the dynamics of polynomial Hénon maps in two. Here we show that these maps all have infinite topological and measure theoretic entropy. The proof also implies the existence of infinitely many periodic orbits of any order greater than two.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Algebra and Number Theory,Analysis,Applied Mathematics,Algebra and Number Theory,Analysis
Reference23 articles.
1. L. Arosio, A. M. Benini, J. E. Fornæss, H. Peters.Dynamics of transcendental Hénon maps, Math. Ann., 373 (2019), 853-894.
2. L. Arosio, A. M. Benini, J. E. Fornæss and H. Peters, Dynamics of transcendental Hénon maps II, preprint, arXiv: 1905.11557.
3. R. L. Adler, A. G. Konheim, M. H. McAndrew.Topological entropy, Trans. Amer. Math. Soc., 114 (1965), 309-319.
4. E. Bedford, M. Lyubich and J. Smillie, Distribution of periodic points of polynomial diffeomorphisms of $\mathbf C^2$, Invent. Math. 114 (1993), no. 2,277–288.,
5. A. M. Benini, J. E. Fornæss, H. Peters.Entropy of transcendental entire functions, Ergodic Theory Dynam. Systems, 41 (2021), 338-348.
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献