Browsing by Author "Coronel, Daniel"
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- ItemHigh-order phase transitions in the quadratic family(2015) Coronel, Daniel; Rivera Letelier, Juan
- ItemLinearly repetitive Delone sets are rectifiable(2013) Aliste Prieto, José; Coronel, Daniel; Gambaudo, Jean-Marc
- ItemModel sets with Euclidean internal space(2023) Allendes Cerda, Mauricio; Coronel, DanielWe 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.
- ItemOn the dynamics of nonreducible cylindrical vortices(OXFORD UNIV PRESS, 2012) Coronel, Daniel; Navas, Andres; Ponce, MarioWe 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.
- ItemSensitive Dependence of Gibbs Measures at Low Temperatures(2015) Coronel, Daniel; Rivera Letelier, Juan
- ItemThe cohomological equation over dynamical systems arising from Delone sets(CAMBRIDGE UNIV PRESS, 2011) Coronel, DanielThe 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.
- ItemTower systems for linearly repetitive Delone sets(CAMBRIDGE UNIV PRESS, 2011) Aliste Prieto, Jose; Coronel, DanielIn 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.