Search results for: LS-FLOWS

• Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces

  Publication

  • M. Izydorek
  • T. O. Rot
  • M. Starostka
  • M. Styborski
  • R. C. Vandervorst

  - JOURNAL OF DIFFERENTIAL EQUATIONS - Year 2017

  In this paper we introduce a new compactness condition — Property-(C) — for flows in (not necessary locally compact) metric spaces. For such flows a Conley type theory can be developed. For example (regular) index pairs always exist for Property-(C) flows and a Conley index can be defined. An important class of flows satisfying the this compactness condition are LS-flows. We apply E-cohomology to index pairs of LS-flows and obtain...

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• Morse inequalities via Conley index theory

  Publication

  • M. Izydorek
  • M. Styborski

  - Year 2011

  The relation known as the Morse inequalities can be extended to a more general setting of flows on a locally compact metric spaces (Conley index) as well as dynamical systems on Hilbert spaces (LS-index). This paper is a discourse around this extension. Except the part concerning the LS-index the material is self-contained and has a character of a survey.

• Topological invariants for equivariant flows: Conley index and degree

  Publication

  • M. Styborski

  - Year 2010

  About forty years have passed since Charles Conley defined the homotopy index. Thereby, he generalized the ideas that go back to the calculus of variations work of Marston Morse. Within this long time the Conley index has proved to be a valuable tool in nonlinear analysis and dynamical systems. A significant development of applied methods has been observed. Later, the index theory has evolved to cover such areas as discrete dynamical...