A survey on partially hyperbolic dynamics
F. Rodriguez Hertz, M. A. Rodriguez Hertz, R. Ures
TL;DR
This survey reviews the current state of research on partially hyperbolic dynamical systems, covering key topics like invariant foliations, ergodicity, and classification, and highlights open problems for future investigation.
Contribution
It provides a comprehensive overview of partially hyperbolic dynamics, summarizing recent advances and identifying unresolved questions across multiple core areas.
Findings
Summarizes key properties of invariant foliations
Highlights progress on ergodicity and transitivity
Proposes open problems for future research
Abstract
Some of the guiding problems in partially hyperbolic systems are the following: (1) Examples, (2) Properties of invariant foliations, (3) Accessibility, (4) Ergodicity, (5) Lyapunov exponents, (6) Integrability of central foliations, (7) Transitivity and (8) Classification. Here we will survey the state of the art on these subjects, and propose related problems.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Advanced Differential Equations and Dynamical Systems