Browsing by Author "Coronel, Daniel"

Now showing 1 - 10 of 10
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    High-order phase transitions in the quadratic family
    (2015) Coronel, Daniel; Rivera Letelier, Juan
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    Linearly repetitive Delone sets are rectifiable
    (2013) Aliste Prieto, José; Coronel, Daniel; Gambaudo, Jean-Marc
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    Low-temperature phase transitions in the quadratic family
    (2013) Coronel, Daniel; Rivera-Letelier, Juan
    We give the first example of a quadratic map having a phase transition after the first zero of the geometric pressure function. This implies that several dimension spectra and large deviation rate functions associated to this map are not (expected to be) real analytic, in contrast to the uniformly hyperbolic case. The quadratic map we study has a non-recurrent critical point, so it is non-uniformly hyperbolic in a strong sense. (c) 2013 Elsevier Inc. All rights reserved.
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    Model sets with Euclidean internal space
    (2023) Allendes Cerda, Mauricio; Coronel, Daniel
    We give a characterization of inter-model sets with Euclidean internal space. This characterization is similar to previous results for general inter-model sets obtained independently by Baake, Lenz and Moody, and Aujogue. The new ingredients are two additional conditions. The first condition is on the rank of the abelian group generated by the set of internal differences. The second condition is on a flow on a torus defined via the address map introduced by Lagarias. This flow plays the role of the maximal equicontinuous factor in the previous characterizations.
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    On the dynamics of nonreducible cylindrical vortices
    (OXFORD UNIV PRESS, 2012) Coronel, Daniel; Navas, Andres; Ponce, Mario
    We study the dynamics of Euclidean isometric extensions of minimal homeomorphisms of compact metric spaces. Under a general hypothesis of homogeneity for the base space, we show that these systems are never minimal, thus extending a classical result of Besicovitch concerning cylindrical cascades. Moreover, using Anosov-Katok-type methods, we construct a topologically transitive isometric extension over an irrational rotation with a two-dimensional fiber.
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    Rapid Convergence to Frequency for Substitution Tilings of the Plane
    (2011) Aliste-Prieto, Jose; Coronel, Daniel; Gambaudo, Jean-Marc
    This paper concerns self-similar tilings of the Euclidean plane. We consider the number of occurrences of a given tile in any domain bounded by a Jordan curve. For a large class of self-similar tilings, including many well-known examples, we give estimates of the oscillation of this number of occurrences around its average frequency times the total number of tiles in the domain, which depend only on the Jordan curve.
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    Robust sensitive dependence of geometric Gibbs states for analytic families of quadratic maps
    (2023) Coronel, Daniel; Rivera-Letelier, Juan
    For quadratic-like maps, we show a phenomenon of sensitive dependence of geometric Gibbs states: There are analytic families of quadratic-like maps for which an arbitrarily small perturbation of the parameter can have a definite effect on the low-temperature geometric Gibbs states. Furthermore, this phenomenon is robust: There is an open set of analytic 2-parameter families of quadratic-like maps that exhibit sensitive dependence of geometric Gibbs states. We introduce a geometric version of the Peierls condition for contour models ensuring that the low-temperature geometric Gibbs states are concentrated near the critical orbit. (c) 2023 Elsevier Inc. All rights reserved.
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    Sensitive Dependence of Gibbs Measures at Low Temperatures
    (2015) Coronel, Daniel; Rivera Letelier, Juan
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    The cohomological equation over dynamical systems arising from Delone sets
    (CAMBRIDGE UNIV PRESS, 2011) Coronel, Daniel
    The hull Omega of an aperiodic repetitive Delone set P in R(d) is a compact metric space on which R(d) acts continuously by translation. Let G be R(m) or T(m) and alpha be a continuous G-cocycle over the dynamical system (Omega, R(d)). In this paper we study conditions under which the cohomological equation alpha(omega, x) = psi(omega - x) - psi has continuous solutions. We give a sufficient condition for general continuous G-cocycles and a necessary condition for transversally locally constant G-cocycles. These conditions are given in terms of the set of first return vectors associated with a tower system for Omega. For linearly repetitive Delone sets we give a necessary and sufficient condition for solving the cohomological equation in the class of transversally Holder G-cocycles.
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    Tower systems for linearly repetitive Delone sets
    (CAMBRIDGE UNIV PRESS, 2011) Aliste Prieto, Jose; Coronel, Daniel
    In this paper we study linearly repetitive Delone sets and prove, following the work of Bellissard, Benedetti and Gambaudo, that the hull of a linearly repetitive Delone set admits a properly nested sequence of box decompositions (tower system) with strictly positive and uniformly bounded (in size and norm) transition matrices. This generalizes a result of Durand for linearly recurrent symbolic systems. Furthermore, we apply this result to give a new proof of a classic estimation of Lagarias and Pleasants on the rate of convergence of patch frequencies.