Connection matrix pairs

David Richeson

Banach Center Publications (1999)

  • Volume: 47, Issue: 1, page 219-232
  • ISSN: 0137-6934

Abstract

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We discuss the ideas of Morse decompositions and index filtrations for isolated invariant sets for both single-valued and multi-valued maps. We introduce the definition of connection matrix pairs and present the theorem of their existence. Connection matrix pair theory for multi-valued maps is used to show that connection matrix pairs obey the continuation property. We conclude by addressing applications to numerical analysis. This paper is primarily an overview of the papers [R1] and [R2].

How to cite

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Richeson, David. "Connection matrix pairs." Banach Center Publications 47.1 (1999): 219-232. <http://eudml.org/doc/208935>.

@article{Richeson1999,
abstract = {We discuss the ideas of Morse decompositions and index filtrations for isolated invariant sets for both single-valued and multi-valued maps. We introduce the definition of connection matrix pairs and present the theorem of their existence. Connection matrix pair theory for multi-valued maps is used to show that connection matrix pairs obey the continuation property. We conclude by addressing applications to numerical analysis. This paper is primarily an overview of the papers [R1] and [R2].},
author = {Richeson, David},
journal = {Banach Center Publications},
keywords = {Conley index; multi-valued maps; connection matrix pairs; Morse decomposition; index filtrations; index filtration; connection matrix},
language = {eng},
number = {1},
pages = {219-232},
title = {Connection matrix pairs},
url = {http://eudml.org/doc/208935},
volume = {47},
year = {1999},
}

TY - JOUR
AU - Richeson, David
TI - Connection matrix pairs
JO - Banach Center Publications
PY - 1999
VL - 47
IS - 1
SP - 219
EP - 232
AB - We discuss the ideas of Morse decompositions and index filtrations for isolated invariant sets for both single-valued and multi-valued maps. We introduce the definition of connection matrix pairs and present the theorem of their existence. Connection matrix pair theory for multi-valued maps is used to show that connection matrix pairs obey the continuation property. We conclude by addressing applications to numerical analysis. This paper is primarily an overview of the papers [R1] and [R2].
LA - eng
KW - Conley index; multi-valued maps; connection matrix pairs; Morse decomposition; index filtrations; index filtration; connection matrix
UR - http://eudml.org/doc/208935
ER -

References

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  1. [C] C. Conley, Isolated Invariant Sets and the Morse Index, CBMS Reg. Conf. Ser. in Math. 38, AMS, Providence, 1978. 
  2. [Fr] J. Franks, Homology and Dynamical Systems, CBMS Reg. Conf. Ser. in Math. 49, AMS, Providence, 1982. 
  3. [F1] R. Franzosa, The Connection Matrix Theory for Morse Decompositions, Trans. AMS 311 (1989), 561-592. Zbl0689.58030
  4. [F2] R. Franzosa, The Continuation Theory For Morse Decompositions and Connection Matrices, Trans. AMS 310 (1988), 781-803. Zbl0708.58021
  5. [FM] R. Franzosa and K. Mischaikow, The Connection Matrix Theory for Semiflows on (Not Necessarily Locally Compact) Metric Spaces, J. Differential Equations 71 (1988), 270-287. Zbl0676.54048
  6. [G1] L. Górniewicz, Homological Methods in Fixed Point Theory of Multi-valued Maps, Dissertationes Mathematicae 129 (1976). Zbl0324.55002
  7. [G2] L. Górniewicz, Topological Degree of Morphisms and its Applications to Differential Inclusions, Raccolta di Seminari del Dipartimento di Matematica dell'Università degli Studi della Calabria 5 (1983). 
  8. [KM1] T. Kaczynski and M. Mrozek, Conley Index for Discrete Multi-valued Dynamical Systems, Top. App. 65 (1995), 83-96. Zbl0843.54042
  9. [KM2] T. Kaczynski and M. Mrozek, Stable Index Pairs for Discrete Dynamical Systems, preprint, 1994. 
  10. [R1] D. Richeson, Connection Matrix Pairs for the Discrete Conley Index, preprint. 
  11. [R2] D. Richeson, Morse Decompositions and Connection Matrix Pairs For Multi-valued Maps, preprint. 

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