On Computer-Assisted Proving The Existence Of Periodic And Bounded Orbits
Copyright policy )On Computer-Assisted Proving The Existence Of Periodic And Bounded Orbits
Abstract We announce a new result on determining the Conley index of the Poincaré map for a time-periodic non-autonomous ordinary differential equation. The index is computed using some singular cycles related to an index pair of a small-step discretization of the equation. We indicate how the result can be applied to computer-assisted proofs of the existence of bounded and periodic solutions. We provide also some comments on computer-assisted proving in dynamics.
- Jagiellonian University Poland
- Polish Academy of Sciences Poland
- Institute of Mathematics Poland
Index theory for dynamical systems, Morse-Conley indices, rigorous numerical algorithm, Periodic orbits of vector fields and flows, Numerical problems in dynamical systems, interval arithmetic, Poincaré map, Approximation methods and numerical treatment of dynamical systems, Conley index
Index theory for dynamical systems, Morse-Conley indices, rigorous numerical algorithm, Periodic orbits of vector fields and flows, Numerical problems in dynamical systems, interval arithmetic, Poincaré map, Approximation methods and numerical treatment of dynamical systems, Conley index
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