Browsing by Author "Rivera Letelier, Juan"
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- ItemChoquet simplices as spaces of invariant probability measures on post-critical sets(ELSEVIER SCIENCE BV, 2010) Isabel Cortez, Maria; Rivera Letelier, JuanA well-known consequence of the ergodic decomposition theorem is that the space of invariant probability Measures of a topological dynamical system, endowed with the weak* topology, is a non-empty metrizable Choquet simplex. We show that every non-empty metrizable Choquet simplex arises as the space of invariant probability measures oil the post-critical set of a logistic map. Here. the post-critical set of a logistic map is the omega-limit set of its unique critical point. In fact we show the logistic map f can be taken in such a way that its post-critical set is a Cantor set where f is minimal, and Such that each invariant probability measure oil this set has zero Lyapunov exponent, and is,in equilibrium state for the potential - In vertical bar f'vertical bar. (C) 2009 Elsevier Masson SAS. All rights reserved.
- ItemEquilibrium states of interval maps for hyperbolic potentials(2014) Li, Huaibin; Rivera Letelier, Juan
- ItemEquilibrium States of Weakly Hyperbolic One-Dimensional Maps for Holder Potentials(2014) Li, Huaibin; Rivera Letelier, Juan
- ItemErgodic theory of rational fractions on ultrametric bodies(WILEY, 2010) Favre, Charles; Rivera Letelier, JuanWe make the first steps towards an understanding of the ergodic properties of a rational map defined over a complete algebraically closed non-archimedean field. For such a rational map R, we construct a natural invariant probability measure (R) which represents the asymptotic distribution of preimages of non-exceptional points. We show that this measure is exponentially mixing, and satisfies the central limit theorem. We prove some general bounds on the metric entropy of (R), and on the topological entropy of R. We finally prove that rational maps with vanishing topological entropy have potential good reduction.
- ItemGeneric parabolic points are isolated in positive characteristic(2016) Lindahl, K.; Rivera Letelier, Juan
- ItemHigh-order phase transitions in the quadratic family(2015) Coronel, Daniel; Rivera Letelier, Juan
- ItemLarge deviation principles for non-uniformly hyperbolic rational maps(CAMBRIDGE UNIV PRESS, 2011) Comman, Henri; Rivera Letelier, JuanWe show some level-2 large deviation principles for rational maps satisfying a strong form of non-uniform hyperbolicity, called 'Topological Collet-Eckmann'. More precisely, we prove a large deviation principle for the distribution of iterated preimages, periodic points, and Birkhoff averages. For this purpose we show that each Holder continuous potential admits a unique equilibrium state, and that the pressure function can be characterized in terms of iterated preimages, periodic points, and Birkhoff averages. Then we use a variant of a general result of Kifer.
- ItemLyapunov spectrum for exceptional rational maps(2013) Gelfert, K.; Przytycki, F.; Rams, M.; Rivera Letelier, Juan
- ItemOn the essential minimum of faltings' height(2018) Burgos Gil, Jose Ignacio; Menares Valencia, Ricardo Alejandro; Rivera Letelier, Juan
- ItemOptimal cycles in ultrametric dynamics and minimally ramified power series(2016) Lindahl, K.; Rivera Letelier, Juan
- Itemp-adic distribution of CM points and Hecke orbits I : Convergence towards the Gauss point(2020) Herrero, S.; Menares Valencia, Ricardo Alejandro; Rivera Letelier, Juan
- ItemSensitive Dependence of Gibbs Measures at Low Temperatures(2015) Coronel, Daniel; Rivera Letelier, Juan
- ItemSTATISTICAL PROPERTIES OF ONE-DIMENSIONAL MAPS UNDER WEAK HYPERBOLICITY ASSUMPTIONS(2014) Rivera Letelier, Juan; Shen, W.
- ItemTHE MAXIMAL ENTROPY MEASURE DETECTS NON-UNIFORM HYPERBOLICITY(INT PRESS BOSTON, INC, 2010) Rivera Letelier, JuanWe characterize two of the most studied non-uniform hyperbolicity conditions for rational maps, semi-hyperbolicity and the topological Collet-Eckmann condition, in terms of the maximal entropy measure.
- ItemTopological orbit equivalence classes and numeration scales of logistic maps(CAMBRIDGE UNIV PRESS, 2012) Isabel Cortez, Maria; Rivera Letelier, JuanWe show that every uniquely ergodic minimal Cantor system is topologically orbit equivalent to the natural extension of a numeration scale associated to a logistic map.