Transversal connecting orbits from shadowing. (English) Zbl 1120.65131
The paper is the last in a series of six works in which the authors analyse, in a fairly sophisticated way, the shadowing phenomenon in the theory of dynamical systems. In this paper they answer the following important question: “Given that one knows a connecting orbit exists, what is a good way to compute it?” In other words, they give “a rigorous method to verify that a numerically computed orbit is shadowed by a true connecting orbit”. The central result is the connecting orbit shadowing theorem. All the details of its proof are provided and hints of its implementation are suggested. Numerical experiments refer to the classical Lorenz model. They underline the effectiveness of the analytic results.
Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca)
MSC:
| 65P20 | Numerical chaos |
| 37C29 | Homoclinic and heteroclinic orbits for dynamical systems |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
Keywords:
homoclinic orbits; heteroclinic orbits; pseudo periodic orbits; pseudo connecting orbits; connecting orbit shadowing; chaotic flow; numerical experiments; Lorenz modelSoftware:
RODESReferences:
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