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math.DS2022
The Arnold conjecture in and the Conley index
L. Asselle, M. Izydorek, M. Starostka
In this paper we give an alternative, purely Conley index based proof of the Arnold conjecture in asserting that a Hamiltonian diffeomorphism of $\mathbb C\m…
math.DS2018
The Maslov Index and the Spectral Flow - revisited
Marek Izydorek, Joanna Janczewska, Nils Waterstraat
We give an elementary proof of a celebrated theorem of Cappell, Lee and Miller which relates the Maslov index of a pair of paths of Lagrangian subspaces to the spectral flow of an…
math.DS2017
Bifurcation of equilibrium forms of an elastic rod on a two-parameter Winkler foundation
Marek Izydorek, Joanna Janczewska, Nils Waterstraat +1
We consider two-parameter bifurcation of equilibrium states of an elastic rod on a deformable foundation. Our main theorem shows that bifurcation occurs if and only if the lineariz…