Search results for: ARNOLD CONJECTURE

• The Arnold conjecture in $ \mathbb C\mathbb P^n $ and the Conley index

  Publication

  • L. Asselle
  • M. Izydorek
  • M. Starostka

  - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B - Year 2023

  n this paper we give an alternative, purely Conley index based proof of the Arnold conjecture in CP^n asserting that a Hamiltonian diffeomorphism of CP^n endowed with the Fubini-Study metric has at least (n+1) fixed points.

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• The E-Cohomological Conley Index, Cup-Lengths and the Arnold Conjecture on T 2n

  Publication

  • M. Starostka
  • N. Waterstraat

  - ADVANCED NONLINEAR STUDIES - Year 2019

  We show that the E-cohomological Conley index, that was introduced by the first author recently, has a natural module structure. This yields a new cup-length and a lower bound for the number of critical points of functionals on Hilbert spaces. When applied to the setting of the Arnold conjecture, this paves the way to a short proof on tori, where it was first shown by C. Conley and E. Zehnder in 1983.

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• E-cohomological Conley index

  Publication

  • M. Starostka

  - Year 2017

  In this thesis we continue with developing the E-cohomological Conley index which was introduced by A.Abbondandolo. In particular, we generalize the index to non-gradient flows, we show that it an possesses additional multiplicative structure and we prove the continuation principle. Then, using continuation principle, we show how the computation of the E-cohomological Conley index can be reduced to the computation of the classical...

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