Blokh, Alexander; Cleveland, Chris; Misiurewicz, Michal 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]. Cited in 4 Documents 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 Keywords:interval maps; smooth maps; piecewise expanding maps; tent map; external rays; invariant luminations; complex polynomials; expanding polymodials; Julia set PDFBibTeX XMLCite \textit{A. Blokh} et al., in: Modern dynamical systems and applications. Dedicated to Anatole Katok on his 60th birthday. Cambridge: Cambridge University Press. 253--270 (2004; Zbl 1147.37335)