Chains without regularity
Alessandro Della Corte, Marco Farotti
TL;DR
This paper investigates chain-recurrence and chain-transitivity in compact dynamical systems without regularity assumptions, establishing fundamental existence results without relying on the Axiom of Choice.
Contribution
It proves that every compact dynamical system contains a chain-recurrent point and a closed, invariant, chain-transitive subsystem without regularity assumptions or the Axiom of Choice.
Findings
Existence of chain-recurrent points in all compact systems
Presence of closed, invariant, chain-transitive subsystems
Results hold without regularity assumptions or Axiom of Choice
Abstract
We study chain-recurrence and chain-transitivity in compact dynamical systems without any regularity assumptions on the map. We prove that every compact system has a chain-recurrent point and a closed, invariant, chain-transitive subsystem. The proofs do not rely on the Axiom of Choice.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Mathematical Dynamics and Fractals · Advanced Operator Algebra Research