Invariant Cantor sets in the parametrized Hénon-Devaney map

Abstract:

We consider the (three parameters) family of nonlinear mappings (Formula presented.) where a, b, c are positive real numbers. (Formula presented.) is the classical Hénon-Devaney map [1, 2, 6]. For a large open region of parameters, we exhibit invariantCantor sets embedded in the plane with two hyperbolic fixed points of saddle type.

Año de publicación:

2022

Keywords:

• Cantor sets
• invariant curves
• maximal invariant sets
• hyperbolic fixed points
• Parametrized Hénon-Devaney map

Fuente:

google

scopus