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Finite Precision Representation of the Conley Decomposition
| Content Provider | Semantic Scholar |
|---|---|
| Author | Hunt, Fern Y. |
| Copyright Year | 1998 |
| Abstract | We present a theoretical basis for a novel way of studying and representing the long time behaviour of nite dimensional maps. It is based on a nite representation of-pseudo orbits of a map by the sample paths of a suitable Markov chain based on a nite partition of phase space. The use of stationary states of the chain and the corresponding partition elements in approximating the attractors of maps and diierential equations was demonstrated in 7] 3] and proved for a class of stable attracting sets in 8]. Here we explore the relationship between the communication classes of the Markov chain and basic sets of the Conley Decomposition of a dy-namical system. We give suucient conditions for the existence of a chain transitive set and show that basic sets are isolated from each other by neighborhoods associated with closed communication classes of the chain. A partition element approximation of an isolating block is introduced that is easy to express in terms of sample paths. Finally in considering the ir-reducibility of the chain, we show that when the map supports an SBR measure there is a unique closed communication class and the Markov chain restricted to those states is irreducible. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://math.nist.gov/~FHunt/publication/fp1.ps.gz |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Approximation Class Conley–Zehnder theorem Existential quantification ISOLATE COMPOUND Irreducibility Map Markov chain Pseudo brand of pseudoephedrine Standard Business Reporting Stationary process sprodiamide |
| Content Type | Text |
| Resource Type | Article |
