Topological-numerical approach to the existence of periodic trajectories in ODE's

zbMath1070.34069MaRDI QIDQ1422582

Paweł Pilarczyk

Publication date: 23 February 2004

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

algorithmperiodic orbitConley indexisolating neighborhoodRössler equations

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Index theory for dynamical systems, Morse-Conley indices (37B30) Numerical methods for ordinary differential equations (65L99)

Related Items (12)

Recent development in rigorous computational methods in dynamical systems ⋮ A Topological Approach to the Algorithmic Computation of the Conley Index for Poincaré Maps ⋮ An implicit algorithm for validated enclosures of the solutions to variational equations for ODEs ⋮ Periodic solutions and invariant torus in the Rössler system ⋮ Finite resolution dynamics ⋮ A numerical verification method for a periodic solution of a delay differential equation ⋮ Use of shrink wrapping for interval Taylor models in algorithms of computer-assisted proof of the existence of periodic trajectories in systems of ordinary differential equations ⋮ Applicability of the interval Taylor model to the computational proof of existence of periodic trajectories in systems of ordinary differential equations ⋮ Coexistence and Dynamical Connections between Hyperchaos and Chaos in the 4D Rössler System: A Computer-Assisted Proof ⋮ Algorithms for constructing isolating sets of phase flows and computer-assisted proofs with the use of interval Taylor models ⋮ Periodic orbits in the Rössler system ⋮ Period doubling in the Rössler system -- a computer assisted proof

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