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math.SG2024
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…
math.SG2022
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…
math.SG2020
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…