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In this paper we investigate how many periodic attractors maps in a small neighbourhood of a given map can have. For this purpose we develop new tools which help to make uniform cross-ratio distortion estimates in a neighbourhood of a map with degenerate critical points.
This paper is concerned with the dynamics of an infinite-dimensional gradient system under small almost periodic perturbations. Under the assumption that the original autonomous system has a global attractor given as the union of unstable manifolds o
We study the dynamics of the periodically-forced May-Leonard system. We extend previous results on the field and we identify different dynamical regimes depending on the strength of attraction $delta$ of the network and the frequency $omega$ of the p
We study the topological properties of attractors of Iterated Function Systems (I.F.S.) on the real line, consisting of affine maps of homogeneous contraction ratio. These maps define what we call a second generation I.F.S.: they are uncountably many
Given a piecewise $C^{1+beta}$ map of the interval, possibly with critical points and discontinuities, we construct a symbolic model for invariant probability measures with nonuniform expansion that do not approach the critical points and discontinui
We prove that a class of one-dimensional maps with an arbitrary number of non-degenerate critical and singular points admits an induced Markov tower with exponential return time asymptotics. In particular the map has an absolutely continuous invarian