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Title: On the iteration of smooth maps
Authors: Correia, Maria de Fátima
Ramos, Carlos
Vinagre, Sandra
Keywords: smooth map
difference equations
symbolic dynamics
discrete dynamical systems
iteration theory
Issue Date: 2010
Publisher: Discrete Dynamics and Difference Equations - Proceedings of the Twelfth International Conference on Difference Equations and Applications, World Scientific Publishing
Citation: M. F. Correia, C. C. Ramos and S. Vinagre, On the iteration of smooth maps, 223-230.
Abstract: Iteration of smooth maps appears naturally in the study of continuous difference equations and boundary value problems. Moreover, it is a subject that may be studied by its own interest, generalizing the iteration theory for interval maps. Our study is motivated by the works of A. N. Sharkovsky et al. [1,3], E. Yu. Romanenko et al. [2], S. Vinagre et al. [4] and R. Severino et al. [5]. We study families of discrete dynamical systems of the type (Ω,f), where Ω is some class of smooth functions, e.g., a sub-class of C^r(J,R), where J is an interval, and f is a smooth map f:R→R. The action is given by ϕ→foϕ. We analyze in particular the case when f is a family of quadratic maps. For this family we analyze the topological behaviour of the system and the parameter dependence on the spectral decomposition of the iterates.
ISBN: 978-981-4287-64-7
Type: article
Appears in Collections:MAT - Artigos em Livros de Actas/Proceedings
CIMA - Artigos em Livros de Actas/Proceedings

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