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8 papers · 2 filters
Mather sets for sequences of matrices and applications to the study of joint spectral radii
Ian D. Morris
The joint spectral radius of a compact set of d-times-d matrices is defined ?to be the maximum possible exponential growth rate of products of matrices drawn from that set. In this…
Decay of correlations for nonuniformly expanding systems with general return times
Ian Melbourne, Dalia Terhesiu
We give a unified treatment of decay of correlations for nonuniformly expanding systems with a good inducing scheme. In addition to being more elementary than previous treatments,…
Statistical Properties and Decay of Correlations for Interval Maps with Critical Points and Singularities
Stefano Luzzatto, Ian Melbourne
We consider a class of piecewise smooth one-dimensional maps with critical points and singularities (possibly with infinite derivative). Under mild summability conditions on the gr…
The topological entropy of Banach spaces
Jozef Bobok, Henk Bruin
We investigate some properties of (universal) Banach spaces of real functions in the context of topological entropy. Among other things, we show that any subspace of whi…
First and higher order uniform dual ergodic theorems for dynamical systems with infinite measure
Ian Melbourne, Dalia Terhesiu
We generalize the proof of Karamata's Theorem by the method of approximation by polynomials to the operator case. As a consequence, we offer a simple proof of \emph{uniform dual er…
Transience and thermodynamic formalism for infinitely branched interval maps
Henk Bruin, Mike Todd
We study a one-parameter family of countably piecewise linear interval maps, which, although Markov, fail the `large image property'. This leads to conservative as well as dissipat…