Schwartzman cycles and ergodic solenoids
Vicente Mu\~noz, Ricardo Perez-Marco
TL;DR
This paper generalizes Schwartzman theory to higher dimensions and unifies it with Ruelle-Sullivan theory using ergodic theorems for solenoid immersions with trapping regions.
Contribution
It extends Schwartzman theory beyond dimension 1 and provides a unified framework with Ruelle-Sullivan theory for solenoid immersions.
Findings
Generalization of Schwartzman theory to higher dimensions
Unified treatment of Schwartzman and Ruelle-Sullivan theories
Application of ergodic theorems to solenoid immersions
Abstract
We extend Schwartzman theory beyond dimension 1 and provide a unified treatment of Ruelle-Sullivan and Schwartzman theories via Birkhoff's ergodic theorem for the class of immersions of solenoids with a trapping region.
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Taxonomy
TopicsCellular Automata and Applications