Distribution in homology classes and discrete fractal dimension

J. H. Everitt, Richard R. Sharp

Type: Article

Publication Date: 2024-05-28

Citations: 0

DOI: https://doi.org/10.1017/prm.2024.67

Abstract

In this note, we examine the proportion of periodic orbits of Anosov flows that lie in an infinite zero density subset of the first homology group. We show that on a logarithmic scale we get convergence to a discrete fractal dimension.

Locations

Proceedings of the Royal Society of Edinburgh Section A Mathematics - View - PDF

Similar Works

Action	Title	Year	Authors
+	Distribution in homology classes and discrete fractal dimension	2023	J. H. Everitt Richard R. Sharp
+	Periodic points and topological entropy of one dimensional maps	1980	Louis Block John Guckenheimer Michał Misiurewicz Lai‐Sang Young
+	Periodic Orbits of Hyperbolic Flows	2004	Richard Sharp
+	Fractal measures and ergodic theory of transcendental meromorphic functions	2008	Janina Kotus Mariusz Urbański
+	Ergodicity, numerical range, and fixed points of holomorphic mappings	2013	Simeon Reich David Shoikhet Jaroslav Zemánek
+	On statistical ω-limit sets in a discrete dynamical system	2021	Bablu Biswas
+	Parallels Between Topological Dynamics and Ergodic Theory	2020	Wen Huang Song Shao Xiangdong Ye
+	Parallels Between Topological Dynamics and Ergodic Theory	2023	Wen Huang Song Shao Xiangdong Ye
+	Bounded Orbits and Fractal Dimension	2017	Aimee Johnson Kathleen Madden Ayşe Şahı̇n
+	Ergodic Theory and Dynamical Systems	2013	Idris Assani
+	On disjointness in topological dynamics and ergodic theory	1979	Joseph Auslander
+ PDF Chat	Density Functions of Periodic Sequences	2022	Olga Anosova Vitaliy Kurlin
+	Omega limit sets and distributional chaos on graphs	2005	Roman Hric Michal Málek
+	Periodic Beurling distributions	1983	Manning G. Collier John A. Kelingos
+	Ergodic theory and topological dynamics	1976	James Russell Brown
+ PDF Chat	Asymptoticity in Topological Dynamics	1954	John D. Baum
+	On sequences of density zero in ergodic theory	1984	Alexandra Bellow Viktor Losert
+ PDF Chat	Harmonic analysis of fractal measures	1996	Palle E. T. Jørgensen Shona Pedersen
+	Hausdorff dimension in quasiregular dynamics	2024	Walter Bergweiler Athanasios Tsantaris
+ PDF Chat	Homology of Closed Orbits of Anosov Flows	1973	J. F. Plante

Works That Cite This (0)

Action	Title	Year	Authors

Works Cited by This (22)

Action	Title	Year	Authors
+	Metric Structures for Riemannian and Non-Riemannian Spaces	2007	Mikhael Gromov
+	A local limit theorem for closed geodesics and homology	2004	Richard Sharp
+	None	2001	Mark Pollicott Richard Sharp
+	Defining Fractal Subsets of <i>Z</i> <sup> <i>d</i> </sup>	1992	Martin T. Barlow S. J. Taylor
+	Geodesics in homology classes	1987	Ralph S. Phillips Peter Sarnak
+	Maximizing entropy for a hyperbolic flow	1973	Rufus Bowen
+ PDF Chat	Precise counting results for closed orbits of Anosov flows	2000	Nalini Anantharaman
+	An Analogue of the Prime Number Theorem for Closed Orbits of Axiom a Flows	1983	William Parry Mark Pollicott
+	Closed orbits in homology classes for Anosov flows	1993	Richard Sharp
+	Lalley's theorem on periodic orbits of hyperbolic flows	1998	Martine Babillot François Ledrappier