Combinatorial vs. classical dynamics: recurrence

DOI10.1016/j.cnsns.2021.106226zbMath1491.37041arXiv2108.13978OpenAlexW4205676442MaRDI QIDQ2076255

Roman Srzednicki, Thomas Wanner, Marian Mrozek, Justin Thorpe

Publication date: 16 February 2022

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.13978

zbMATH Keywords

periodic orbitConley indexisolated invariant setcombinatorial vector field

Mathematics Subject Classification ID

General topology of complexes (57Q05) Triangulating manifolds (57Q15) Periodic orbits of vector fields and flows (37C27) Index theory for dynamical systems, Morse-Conley indices (37B30) Combinatorial dynamics (types of periodic orbits) (37E15) Periodic and quasi-periodic flows and diffeomorphisms (37C55)

Related Items

On the dynamics of the combinatorial model of the real line ⋮ Stability and constructions of the Poincaré maps for a class of stochastic partial differential equations ⋮ Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces

Uses Software

• INTLAB

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Towards a formal tie between combinatorial and classical vector field dynamics
• Lectures on algebraic topology.
• Conley-Morse-Forman theory for combinatorial multivector fields on Lefschetz complexes
• Delay equations. Functional-, complex-, and nonlinear analysis
• Zeta functions, periodic trajectories, and the Conley index
• Linking combinatorial and classical dynamics: Conley index and Morse decompositions
• Creating semiflows on simplicial complexes from combinatorial vector fields
• Algebraic topology of finite topological spaces and applications
• A Lefschetz fixed point theorem for multivalued maps of finite spaces
• Local semi-dynamical systems
• Polygonal approximation of flows
• Note on trajectories in a solid torus
• Chaos in the Lorenz equations: a computer-assisted proof
• Chaos in the Lorenz equations: A computer assisted proof. Part II: Details
• Reducibility among Combinatorial Problems
• A Database Schema for the Analysis of Global Dynamics of Multiparameter Systems
• The Lorenz Attractor, a Paradigm for Chaos
• On the Surface of Section and Periodic Trajectories
• Chaos in the Lorenz equations: A computer assisted proof. III: Classical parameter values