Abstract. The parameter space S p for monic centered cubic polynomial maps with a marked critical point of period p is a smooth affine algebraic curve whose genus increases rapidly with p. Each S p consists of a compact connectedness locus together with finitely many escape regions, each of which is biholomorphic to a punctured disk and is characterized by an essentially unique Puiseux series. This note will describe the topology of S p , and of its smooth compactification, in terms of these escape regions. In particular, it computes the Euler characteristic. It concludes with a discussion of the real sub-locus of S p .
Abstract. We study a counting problem in holomorphic dynamics related to external rays of complex polynomials. We give upper bounds on the number of external rays that land at a point z in the Julia set of a polynomial, provided that z has an infinite forward orbit.
Abstract. We discuss rescaling limits for sequences of complex rational maps in one variable which approach infinity in parameter space. It is shown that any given sequence of maps of degree d ≥ 2 has at most 2d − 2 dynamically distinct rescaling limits which are not postcritically finite. For quadratic rational maps, a complete description of the possible rescaling limits is given. These results are obtained employing tools from nonArchimedean dynamics.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.