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Expanding polymodials. (English) Zbl 1147.37335

Brin, Michael (ed.) et al., Modern dynamical systems and applications. Dedicated to Anatole Katok on his 60th birthday. Cambridge: Cambridge University Press (ISBN 0-521-84073-2/hbk). 253-270 (2004).
Summary: We investigate what happens when we trade analyticity of complex polynomials for expansion properties, similarly as for piecewise expanding maps versus smooth maps in real dimension one. We get a class of maps that we call expanding polymodials. We investigate their properties, that turn out to be similar to those of complex polynomials. After introducing the Julia set and proving its basic properties, we concentrate on the case when the Julia set is connected. The other case, as well as the other aspects of the theory, will be addressed in forthcoming papers.
For the entire collection see [Zbl 1051.00012].

MSC:

37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
37E05 Dynamical systems involving maps of the interval
57M12 Low-dimensional topology of special (e.g., branched) coverings
37F15 Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems
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