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math.DS2015★ 1 cited
Almost sure convergence of maxima for chaotic dynamical systems
M. P. Holland, M. Nicol, A. Török
Suppose is a measure preserving dynamical system and is an observable with some degree of regularity. We investigate the maximum pr…
math.DS2014
Quantitative recurrence statistics and convergence to an extreme value distribution for non-uniformly hyperbolic dynamical systems
Mark Holland, Pau Rabassa, Alef Sterk
For non-uniformly hyperbolic dynamical systems we consider the time series of maxima along typical orbits. Using ideas based upon quantitative recurrence time statistics we prove c…
math.DS2007
Statistical properties of one-dimensional maps with critical points and singularities
K. Díaz-Ordaz, M. P. Holland, S. Luzzatto
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 as…