Abstract
AbstractTranscendental Hénon maps are the natural extensions of the well investigated complex polynomial Hénon maps to the much larger class of holomorphic automorphisms. We prove here that transcendental Hénon maps always have non-trivial dynamical behavior, namely that they always admit both periodic and escaping orbits, and that their Julia sets are non-empty and perfect.
Publisher
Springer Science and Business Media LLC
Reference12 articles.
1. Arosio, L., Benini, A.M., Erik Fornæss, J., Peters, H.: Dynamics of transcendental Hénon maps. Math. Ann. 373(1–2), 852–894 (2019)
2. Arosio, L., Lárusson, F.: Chaotic holomorphic automorphisms of Stein manifolds with the volume density property. J. Geom. Anal. 29(2), 1744–1762 (2019)
3. Bedford, E., Smillie, J.: Polynomial diffeomorphisms of $$\mathbb{c}^2$$: critical points and Lyapunov exponents. J. Geom. Anal. 8(4), 349–383 (1998)
4. Eremenko, A.E.: On the Iteration of Entire Functions, pp. 339–345. Banach Center Publications, Warsaw (1989)
5. Fornaess, J.E., Sibony, N.: The closing lemma for holomorphic maps. Ergod. Theory Dyn. Syst. 17(4), 821–837 (1997)
Cited by
2 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