7 papers
Morse homology for a class of elliptic partial differential equations
L. Asselle, S. Cingolani, M. Starostka
In this paper we show that a notion of non-degeneracy which allows to develop Morse theory is generically satisfied for a large class of -functionals defined on Banach spaces.…
On the degenerate Arnold conjecture on
L. Asselle, M. Starostka
In the 1960s Arnold conjectured that a Hamiltonian diffeomorphism of a closed connected symplectic manifold should have at least as many contractible fixed points as a smoo…
A note on the Morse homology for a class of functionals in Banach spaces involving the -Laplacian
L. Asselle, M. Starostka
In this paper we show how to construct Morse homology for an explicit class of functionals involving the -Laplacian. The natural domain of definition of such functionals is the…
Morse homology for the Hamiltonian action in cotangent bundles
L. Asselle, M. Starostka
In this paper we use the gradient flow equation introduced in [10] to construct a Morse complex for the Hamiltonian action on a mixed regularity space of loops in the…
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 Palais-Smale condition for the Hamiltonian action on a mixed regularity space of loops in cotangent bundles and applications
Luca Asselle, Maciej Starostka
We show that the Hamiltonian action satisfies the Palais-Smale condition over a "mixed regularity" space of loops in cotangent bundles, namely the space of loops with regularity $H…
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…