Leray functor and cohomological Conley index for discrete dynamical systems
نویسندگان
چکیده
منابع مشابه
Conley Index for Discrete Multivalued Dynamical Systems
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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Conley index theory is a very powerful tool in the study of dynamical systems, differential equations and bifurcation theory. In this paper, we make an attempt to generalize the Conley index to discrete random dynamical systems. And we mainly follow the Conley index for maps given by Franks and Richeson in [6]. Furthermore, we simply discuss the relations of isolated invariant sets between time...
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The Conley index is a topological tool used in the qualitative theory of differential equations and dynamical systems (see [1], [10], [4]). In the simplest setting it takes the form of an object of a certain category (homotopy category of metric spaces, category of graded moduli etc.), which is known up to an isomorphism. This lack of precision is caused by the fact that there are many so calle...
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We present a scheme for constructing various Conley indices for locally defined maps. In particular, we extend the shape index of Robbin and Salamon to the case of a locally defined map in a locally compact Hausdorff space. We compare the shape index with the cohomological Conley index for maps. We also prove the commutativity property of the Conley index, which is analogous to the commutativit...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1990
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1990-0968888-1