Directional transition matrix

Hiroshi Kokubu; Konstantin Mischaikow; Hiroe Oka

Banach Center Publications (1999)

  • Volume: 47, Issue: 1, page 133-144
  • ISSN: 0137-6934

Abstract

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We present a generalization of topological transition matrices introduced in [6].

How to cite

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Kokubu, Hiroshi, Mischaikow, Konstantin, and Oka, Hiroe. "Directional transition matrix." Banach Center Publications 47.1 (1999): 133-144. <http://eudml.org/doc/208929>.

@article{Kokubu1999,
abstract = {We present a generalization of topological transition matrices introduced in [6].},
author = {Kokubu, Hiroshi, Mischaikow, Konstantin, Oka, Hiroe},
journal = {Banach Center Publications},
keywords = {Conley index; connection matrix; transition matrix; fast-slow systems},
language = {eng},
number = {1},
pages = {133-144},
title = {Directional transition matrix},
url = {http://eudml.org/doc/208929},
volume = {47},
year = {1999},
}

TY - JOUR
AU - Kokubu, Hiroshi
AU - Mischaikow, Konstantin
AU - Oka, Hiroe
TI - Directional transition matrix
JO - Banach Center Publications
PY - 1999
VL - 47
IS - 1
SP - 133
EP - 144
AB - We present a generalization of topological transition matrices introduced in [6].
LA - eng
KW - Conley index; connection matrix; transition matrix; fast-slow systems
UR - http://eudml.org/doc/208929
ER -

References

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  1. [1] L. Arnold, C. Jones, K. Mischaikow, G. Raugel, Dynamical Systems Montecatini Terme 1994 (ed. R. Johnson), Lecture Notes in Math., Vol. 1609, Springer, 1995. 
  2. [2] C. Conley, Isolated Invariant Sets and the Morse Index, CBMS Reg. Conf. Ser. in Math., 38, AMS, Providence, 1978. 
  3. [3] R. Franzosa, The connection matrix theory for Morse decompositions, Trans. AMS 311 (1989) 781-803. Zbl0708.58021
  4. [4] T. Gedeon, H. Kokubu, K. Mischaikow, H. Oka, and J. Reineck, Conley index theory for fast-slow systems, I: One dimensional slow dynamics, to appear in J. Dynam. Diff. Eq. Zbl0945.34029
  5. [5] H. Kokubu, K. Mischaikow, and H. Oka, Existence of infinitely many connecting orbits in a singularly perturbed ordinary differential equations, Nonlinearity 9 (1996), 1263-1280. Zbl0898.34047
  6. [6] C. McCord and K. Mischaikow, Connected simple systems, transition matrices and heteroclinic bifurcations, Trans. A.M.S. 333 (1992), 397-422. Zbl0763.34028
  7. [7] C. McCord and K. Mischaikow, Equivalence of topological and singular transition matrices in the Conley index, Mich. Math. J. 42 (1995), 387-414. Zbl0853.58080
  8. [8] K. Mischaikow. M. Mrozek and J. Reineck, Singular index pairs, to appear in J. Dynam. Diff. Eq. Zbl0943.34028
  9. [9] J. Reineck, The connection matrix in Morse-Smale flows, Trans. A.M.S. 322 (1990), 523-545. Zbl0714.58027
  10. [10] J. Reineck, Connecting orbits in one-parameter families of flows, Ergod. Th. & Dynam. Sys. 8* (1988), 359-374. Zbl0675.58034

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