# Index filtrations and Morse decompositions for discrete dynamical systems

Annales Polonici Mathematici (1999)

- Volume: 72, Issue: 1, page 51-70
- ISSN: 0066-2216

## Access Full Article

top## Abstract

top## How to cite

topBartłomiejczyk, P., and Dzedzej, Z.. "Index filtrations and Morse decompositions for discrete dynamical systems." Annales Polonici Mathematici 72.1 (1999): 51-70. <http://eudml.org/doc/262787>.

@article{Bartłomiejczyk1999,

abstract = {On a Morse decomposition of an isolated invariant set of a homeomorphism (discrete dynamical system) there are partial orderings defined by the homeomorphism. These are called admissible orderings of the Morse decomposition. We prove the existence of index filtrations for admissible total orderings of a Morse decomposition and introduce the connection matrix in this case.},

author = {Bartłomiejczyk, P., Dzedzej, Z.},

journal = {Annales Polonici Mathematici},

keywords = {Conley index; index filtration; Morse decomposition; connection matrix; index filtrations; index triple},

language = {eng},

number = {1},

pages = {51-70},

title = {Index filtrations and Morse decompositions for discrete dynamical systems},

url = {http://eudml.org/doc/262787},

volume = {72},

year = {1999},

}

TY - JOUR

AU - Bartłomiejczyk, P.

AU - Dzedzej, Z.

TI - Index filtrations and Morse decompositions for discrete dynamical systems

JO - Annales Polonici Mathematici

PY - 1999

VL - 72

IS - 1

SP - 51

EP - 70

AB - On a Morse decomposition of an isolated invariant set of a homeomorphism (discrete dynamical system) there are partial orderings defined by the homeomorphism. These are called admissible orderings of the Morse decomposition. We prove the existence of index filtrations for admissible total orderings of a Morse decomposition and introduce the connection matrix in this case.

LA - eng

KW - Conley index; index filtration; Morse decomposition; connection matrix; index filtrations; index triple

UR - http://eudml.org/doc/262787

ER -

## References

top- [C] C. Conley, Isolated Invariant Sets and the Morse Index, CBMS Regional Conf. Ser. in Math. 38, Amer. Math. Soc., Providence, 1980.
- [CoZ] C. Conley and R. Zehnder, Morse-type index theory for flows and periodic solutions for Hamiltonian systems, Comm. Pure Appl. Math. 37 (1984), 207-253. Zbl0559.58019
- [Fra1] R. Franzosa, Index filtrations and the homology index braid for partially ordered Morse decompositions, Trans. Amer. Math. Soc. 298 (1986), 193-213. Zbl0626.58013
- [Fra2] R. Franzosa, The connection matrix theory for Morse decompositions, ibid. 311 (1989), 561-592. Zbl0689.58030
- [Mr1] M. Mrozek, Index pairs and the fixed point index for semidynamical systems with discrete time, Fund. Math. 133 (1989), 179-194. Zbl0708.58024
- [Mr2] M. Mrozek, Leray functor and cohomological Conley index for discrete dynamical systems, Trans. Amer. Math. Soc. 318 (1990), 149-178. Zbl0686.58034
- [Mr3] M. Mrozek, Morse equation in Conley's index theory for homeomorphisms, Topology Appl. 38 (1991), 45-60. Zbl0725.58022
- [Re] J. Reineck, The connection matrix in Morse-Smale flows II, Trans. Amer. Math. Soc. 347 (1995), 2097-2110. Zbl0831.58031
- [Ri] D. Richeson, Connection matrix pairs for the discrete Conley index, ibid., to appear.
- [Sal] D. Salamon, Connected simple systems and the Conley index of isolated invariant sets, ibid. 291 (1985), 1-41.
- [Szy] A. Szymczak, The Conley index for discrete dynamical systems, Topology Appl. 66 (1995), 215-240. Zbl0840.34043

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.