The authors develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped with a sub-Riemannian metric. In particular, they develop ...the thermodynamic formalism and show that, under natural hypotheses, the limit set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen's parameter. They illustrate their results for a variety of examples of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the non-real classical rank one hyperbolic spaces.
This volume contains the proceedings of the AMS Special Session on Unimodularity in Randomly Generated Graphs, held from October 8-9, 2016, in Denver, Colorado. Unimodularity, a term initially used ...in locally compact topological groups, is one of the main examples in which the generalization from groups to graphs is successful. The "randomly generated graphs", which include percolation graphs, random Erdős-Rényi graphs, and graphings of equivalence relations, are much easier to describe if they result as random objects in the context of unimodularity, with respect to either a vertex-transient "host"-graph or a probability measure. This volume tries to give an impression of the various fields in which the notion currently finds strong development and application: percolation theory, point processes, ergodic theory, and dynamical systems.
This volume contains the proceedings of three conferences in Ergodic Theory and Symbolic Dynamics: the Oxtoby Centennial Conference, held from October 30-31, 2010, at Bryn Mawr College; the Williams ...Ergodic Theory Conference, held from July 27-29, 2012, at Williams College; and the AMS Special Session on Ergodic Theory and Symbolic Dynamics, held from January 17-18, 2014, in Baltimore, MD. This volume contains articles covering a variety of topics in measurable, symbolic and complex dynamics. It also includes a survey article on the life and work of John Oxtoby, providing a source of information about the many ways Oxtoby's work influenced mathematical thought in this and other fields.
This volume is a tribute to one of the founders of modern theory of dynamical systems, the late Dmitry Victorovich Anosov.It contains both original papers and surveys, written by some distinguished ...experts in dynamics, which are related to important themes of Anosov's work, as well as broadly interpreted further crucial developments in the theory of dynamical systems that followed Anosov's original work.Also included is an article by A. Katok that presents Anosov's scientific biography and a picture of the early development of hyperbolicity theory in its various incarnations, complete and partial, uniform and nonuniform.
This volume contains the proceedings of the Second Workshop of Mexican Mathematicians Abroad (II Reunion de Matematicos Mexicanos en el Mundo), held from December 15-19, 2014, at Centro de ...Investigacion en Matematicas (CIMAT) in Guanajuato, Mexico.This meeting was the second in a series of ongoing biannual meetings aimed at showcasing the research of Mexican mathematicians based outside of Mexico.The book features articles drawn from eight broad research areas: algebra, analysis, applied mathematics, combinatorics, dynamical systems, geometry, probability theory, and topology. Their topics range from novel applications of non-commutative probability to graph theory, to interactions between dynamical systems and geophysical flows.Several articles survey the fields and problems on which the authors work, highlighting research lines currently underrepresented in Mexico. The research-oriented articles provide either alternative approaches to well-known problems or new advances in active research fields. The wide selection of topics makes the book accessible to advanced graduate students and researchers in mathematics from different fields.This book is published in cooperation with Sociedad Matematica Mexicana.
On the ergodic theory of impulsive semiflows Afonso, S.M.; Bonotto, E.M.; Siqueira, J.
Journal of mathematical analysis and applications,
12/2024, Letnik:
540, Številka:
2
Journal Article
Recenzirano
In this work, we established a simpler criterion for the existence of invariant measures for impulsive semiflows. In addition, we exhibit sufficient conditions to obtain a Variational Principle and ...the existence and uniqueness of equilibrium states. Some examples are provided to illustrate the theory developed.
This volume contains the proceedings of the 16th Carolina Dynamics Symposium, held from April 13-15, 2018, at Agnes Scott College, Decatur, Georgia.The papers cover various topics in dynamics and ...randomness, including complex dynamics, ergodic theory, topological dynamics, celestial mechanics, symbolic dynamics, computational topology, random processes, and regular languages.The intent is to provide a glimpse of the richness of the field and of the common threads that tie the different specialties together.
The so-called "pinched disk" model of the Mandelbrot set is due to A. Douady, J. H. Hubbard and W. P. Thurston. It can be described in the language of geodesic laminations. The combinatorial model is ...the quotient space of the unit disk under an equivalence relation that, loosely speaking, "pinches" the disk in the plane (whence the name of the model). The significance of the model lies in particular in the fact that this quotient is planar and therefore can be easily visualized. The conjecture that the Mandelbrot set is actually homeomorphic to this model is equivalent to the celebrated MLC conjecture stating that the Mandelbrot set is locally connected. For parameter spaces of higher degree polynomials no combinatorial model is known. One possible reason may be that the higher degree analog of the MLC conjecture is known to be false. The authors investigate to which extent a geodesic lamination is determined by the location of its critical sets and when different choices of critical sets lead to essentially the same lamination. This yields models of various parameter spaces of laminations similar to the "pinched disk" model of the Mandelbrot set.
