The Conley index for fast–slow systems II: Multidimensional slow variable
نویسندگان
چکیده
منابع مشابه
The Conley index for fast-slow systems II: Multi-dimensional slow variable
We use Conley index theory to develop a general method used to prove existence of periodic and heteroclinic orbits in a singularly perturbed system of ODE’s. This is a continuation of the authors’ earlier work [9] which Supported by NSF Grant INT-0089631 and by JSPS Japan-U.S. Cooperative Science Program. Partially supported by NSF EIA-BITS grant 426411. Partially supported by Grant-in-Aid for ...
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Geometric Singular Perturbation Theory (GSPT) and Conley Index Theory are two powerful techniques to analyze dynamical systems. Conley already realized that using his index is easier for singular perturbation problems. In this paper, we will revisit Conley’s results and prove that the GSPT technique of Fenichel Normal Form can be used to simplify the application of Conley index techniques even ...
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The deenitions of isolating block, index pair, and the Conley index, together with the proof of homotopy and additivity properties of the index are generalized for discrete multivalued dynamical systems. That generalization provides a theoretical background of numerical computation used by Mischaikow and Mrozek in their computer assisted proof of chaos in the Lorenz equations, where nitely repr...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2006
ISSN: 0022-0396
DOI: 10.1016/j.jde.2005.11.006