On computer-assisted proving the existence of periodic and bounded orbits. (English) Zbl 1373.37041
Summary: 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.
MSC:
| 37B30 | Index theory for dynamical systems, Morse-Conley indices |
| 37C27 | Periodic orbits of vector fields and flows |
| 37M99 | Approximation methods and numerical treatment of dynamical systems |
| 65P99 | Numerical problems in dynamical systems |
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