7 papers
On the Uniqueness of the -Equivariant Spectral Flow
Marek Izydorek, Joanna Janczewska, Maciej Starostka +1
The spectral flow is an integer-valued homotopy invariant for paths of selfadjoint Fredholm operators. Lesch as well as Pejsachowicz, Fitzpatrick and Ciriza independently showed th…
The Equivariant Spectral Flow and Bifurcation for Functionals with Symmetries -- Part I
Marek Izydorek, Joanna Janczewska, Maciej Starostka +1
We consider bifurcation of critical points from a trivial branch for families of functionals that are invariant under the orthogonal action of a compact Lie group. Based on a recen…
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…
The Equivariant Spectral Flow and Bifurcation of Periodic Solutions of Hamiltonian Systems
Marek Izydorek, Joanna Janczewska, Nils Waterstraat
We define a spectral flow for paths of selfadjoint Fredholm operators that are equivariant under the orthogonal action of a compact Lie group as an element of the representation ri…
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…
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…
Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces
Marek Izydorek, Thomas O. Rot, Maciej Starostka +2
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 devel…