Zobrazeno 1 - 10
of 89
pro vyhledávání: '"Sara Munday"'
By connecting dynamical systems and number theory, this graduate textbook on ergodic theory acts as an introduction to a highly active area of mathematics, where a variety of strands of research open up. The text explores various concepts in infinite
Autor:
Andrei E. Ghenciu, Sara Munday
Publikováno v:
Journal of Number Theory. 228:359-374
In this paper, we look at a family of Renyi-like continued fraction expansions and the associated conformal iterated function systems. We show that for every k ≥ 2 , every such associated system has full Hausdorff dimension spectrum. We construct t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f26d1bc0a475c2fe587d8f2db6a0d9d6
https://doi.org/10.1016/j.jnt.2021.04.001
https://doi.org/10.1016/j.jnt.2021.04.001
A slow triangle map with a segment of indifferent fixed points and a complete tree of rational pairs
Publikováno v:
Monatshefte für Mathematik. 194:1-40
We study the two-dimensional continued fraction algorithm introduced in \cite{garr} and the associated \emph{triangle map} $T$, defined on a triangle $\triangle\subset \R^2$. We introduce a slow version of the triangle map, the map $S$, which is ergo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a180723b980006160dc79742b5c8f0c8
https://doi.org/10.1007/s00605-020-01500-w
https://doi.org/10.1007/s00605-020-01500-w
Complex dynamics is one of the most fascinating subjects of study and research in mathematics. This third volume in the series entitled Non-Invertible Dynamical Systems not only examines topological and analytical properties of the iteration of ratio
As a natural counterpart to Nakada's $\alpha$-continued fraction maps, we study a one-parameter family of continued fraction transformations with an indifferent fixed point. We prove that matching holds for Lebesgue almost every parameter in this fam
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::78ee25372432c5e343ef85676887977b
http://hdl.handle.net/1887/3201452
http://hdl.handle.net/1887/3201452
This book consists of three volumes. The first volume contains introductory accounts of topological dynamical systems, fi nite-state symbolic dynamics, distance expanding maps, and ergodic theory of metric dynamical systems acting on probability meas
The book contains a detailed treatment of thermodynamic formalism on general compact metrizable spaces. Topological pressure, topological entropy, variational principle, and equilibrium states are presented in detail. Abstract ergodic theory is also
Publikováno v:
Journal of Number Theory. 175:223-249
In this paper, we consider two dynamical systems associated to the nearest integer continued fraction, and show that both of them have full Hausdorff dimension spectrum.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cba3a6068a90946d83ad2e43c91bac65
https://doi.org/10.1016/j.jnt.2016.09.002
https://doi.org/10.1016/j.jnt.2016.09.002
Autor:
Sara Munday, Jun-Jie Miao
Publikováno v:
Discrete & Continuous Dynamical Systems - S. 10:353-365
In this paper we first give a survey of known results on the derivative of slippery Devil's staircase functions, that is, functions that are singular with respect to the Lebesgue measure and strictly increasing. The best known example of such a funct
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::49d5d6c91034110622bdc9664f8a994e
https://doi.org/10.3934/dcdss.2017017
https://doi.org/10.3934/dcdss.2017017