Transcendental Henon maps are the natural extensions of the well investigated complex polynomial Henon maps to the much larger class of holomorphic automorphisms. We prove here that transcendental Henon 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.
Arosio, L., Miriam Benini, A., Erik Forn??ss, J., Peters, H. (2023). Dynamics of transcendental Hénon maps-II. MATHEMATISCHE ANNALEN, 385(3-4) [10.1007/s00208-022-02358-z].
Dynamics of transcendental Hénon maps-II
Leandro Arosio;
2023-01-01
Abstract
Transcendental Henon maps are the natural extensions of the well investigated complex polynomial Henon maps to the much larger class of holomorphic automorphisms. We prove here that transcendental Henon 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.File in questo prodotto:
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