An algorithmic approach to the Conley index theory. (English) Zbl 0941.37004
The paper is devoted to the following questions:
(1) Can the techniques which were developed to prove chaos in the Lorenz system be applied to other problems in differential equations?
(2) For a given continuous dynamical system and a compact set, is it possible to verify in finite time whether the set is an isolating neighborhood?
To this end the author introduces a class of representable sets and multivalued representable maps which may be performed by an algorithm. Using these objects the author investigates questions (1) and (2) mentioned above.
(1) Can the techniques which were developed to prove chaos in the Lorenz system be applied to other problems in differential equations?
(2) For a given continuous dynamical system and a compact set, is it possible to verify in finite time whether the set is an isolating neighborhood?
To this end the author introduces a class of representable sets and multivalued representable maps which may be performed by an algorithm. Using these objects the author investigates questions (1) and (2) mentioned above.
Reviewer: Messoud Efendiev (Berlin)
MSC:
| 37B30 | Index theory for dynamical systems, Morse-Conley indices |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
