Filled Julia set of some class of Hénon-like maps. (English) Zbl 1439.37050
Summary: In this work we consider a class of endomorphisms of \(\mathbb{R}^2\) defined by \(f(x,y)=(xy+c,x)\), where \(c \in \mathbb{R}\) is a real number and we prove that when \(-1 < c < 0\), the forward filled Julia set of \(f\) is the union of stable manifolds of fixed and 3-periodic points of \(f\). We also prove that the backward filled Julia set of \(f\) is the union of unstable manifolds of the saddle fixed and 3-periodic points of \(f\).
MSC:
| 37F44 | Holomorphic families of dynamical systems; holomorphic motions; semigroups of holomorphic maps |
| 37F10 | Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets |
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