Robust dynamics, invariant structures and topological classification

2018/02/14 by Potrie, Rafael
#Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1802.05291

Abstract

This text is about geometric structures imposed by robust dynamical behaviour. We explain recent results towards the classification of partially hyperbolic systems in dimension 3 using the theory of foliations and its interaction with topology. We also present recent examples which introduce a challenge in the classification program and we propose some steps to continue this classification. Finally, we give some suggestions on what to do after classification is achieved.

Related

• A survey on partially hyperbolic dynamics
• Algorithms and topological invariants for dynamic systems. I. Basic definitions
• Algorithms and topological invariants for dynamic systems. III. Algorithms for Recognition and Classification of 2-Dimensional Surfaces
• Algorithms and topological invariants for dynamic systems. II. Discrete Structures
• Geometric Expansions, Lyapunov Exponents and Foliations