Chaos for foliated spaces and pseudogroups

2022/02/21 by Ramón Barral Lijó, Lijó, Ramón Barral
Computer Science · Mathematics · Physics and Astronomy · #37B02 37B05 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2202.09983

openalex publication_date 2022/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize "sensitivity to initial conditions" to foliated spaces and pseudogroups, offering a definition of Devaney chaos in this setting. In contrast to the case of group actions, where sensitivity follows from the other two conditions of Devaney chaos, we show that this is true only for compact foliated spaces, exhibiting a counterexample in the non-compact case. Finally, we obtain an analogue of the Auslander-Yorke dichotomy for compact foliated spaces and compactly generated pseudogroups.

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