Nonwandering set of points of skew-product maps with base having closed set of periodic points |
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| Authors: | Juan Luis Garcí a Guirao,Raquel Garcí a Rubio, |
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| Affiliation: | aDepartamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Hospital de Marina, 30203-Cartagena (Región de Murcia), Spain;bDepartamento de Matemática Aplicada, Universidad de Alicante, San Vicente del Raspeig s/n (Comunidad Valenciana), Spain |
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| Abstract: | The aim of the present paper is to study the structure of the nonwandering set of points Ω( ) for the skew-product maps  of the unit square  , (x,y)→(f(x),g(x,y)), with base f having closed set of periodic points. For every  and every point (x,y) with x periodic of period px by f and y not chain recurrent of Fpx|Ix, where  , we prove that (x,y) Ω(F). On the other hand we construct a map  with an isolated fixed point x0 of f and y0Ω(F|Ix0) such that (x0,y0) Ω(F0). |
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| Keywords: | Discrete dynamical system Skew-product map Nonwandering point |
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