On the computation of extended rescaled Poincaré maps for singular vector fields

DOI10.1080/14689367.2019.1665625zbMath1447.37030OpenAlexW2972801153MaRDI QIDQ3298335

Qianying Xiao, Yiwei Zhang

Publication date: 14 July 2020

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/14689367.2019.1665625

zbMATH Keywords

Poincaré mapssingular vector fieldsaperiodic singular chain

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Dynamics induced by flows and semiflows (37C10) Index theory for dynamical systems, Morse-Conley indices (37B30) Dynamical systems involving smooth mappings and diffeomorphisms (37C05) Dynamical systems with singularities (billiards, etc.) (37C83) Symmetries and invariants of dynamical systems (37C79)

Cites Work

• Birth of homoclinic intersections: a model for the central dynamics of partially hyperbolic systems
• \(C^1\) weak Palis conjecture for nonsingular flows
• Singularities of vector fields
• Robustly transitive singular sets via approach of an extended linear Poincaré flow
• Morse-Smale systems and horseshoes for three dimensional singular flows
• Invariant manifolds
• Unnamed Item