2 citations · 3 across the 9 of their papers we have counts for
9 papers
Topics in Symplectic Dynamics: Barcode Entropy
Erman Cineli, Viktor L. Ginzburg, Basak Z. Gurel +1
Barcode entropy is an invariant of a Hamiltonian system -- a Hamiltonian diffeomorphism or a Reeb flow -- measuring its Morse or Floer theoretic complexity at a small scale. More s…
Equivariant critical point theory and bifurcation of gravity-capillary Stokes waves
Tommaso Barbieri, Massimiliano Berti, Marco Mazzucchelli
We establish novel existence results of gravity-capillary periodic traveling waves. In particular we prove the bifurcation of multiple, geometrically distinct truly Stoke…
Length spectrum rigidity and flexibility of spheres of revolution with one equator
Alberto Abbondandolo, Marco Mazzucchelli
We define a notion of marked length spectrum for -symmetric Riemannian metrics on the two-sphere having only one equator. We prove that isospectral metrics in this class have…
Bifurcation of gravity-capillary Stokes waves with constant vorticity
T. Barbieri, M. Berti, A. Maspero +1
We consider the gravity-capillary water waves equations of a 2D fluid with constant vorticity. By employing variational methods we prove the bifurcation of periodic traveling water…
From curve shortening to flat link stability and Birkhoff sections of geodesic flows
Marcelo R. R. Alves, Marco Mazzucchelli
We employ the curve shortening flow to establish three new results on the dynamics of geodesic flows of closed Riemannian surfaces. The first one is the stability, under -smal…
Closed geodesics and the first Betti number
Gonzalo Contreras, Marco Mazzucchelli
We prove that, on any closed manifold of dimension at least two with non-trivial first Betti number, a generic Riemannian metric has infinitely many closed geodesics, an…
On potentials whose level sets are orbits
Philippe Bolle, Marco Mazzucchelli, Andrea Venturelli
A level orbit of a mechanical Hamiltonian system is a solution of Newton equation that is contained in a level set of the potential energy. In 2003, Mark Levi asked for a character…
On the Barcode Entropy of Reeb Flows
Erman Cineli, Viktor L. Ginzburg, Basak Z. Gurel +1
In this paper we continue investigating connections between Floer theory and dynamics of Hamiltonian systems, focusing on the barcode entropy of Reeb flows. Barcode entropy is the…
Invariant Sets and Hyperbolic Closed Reeb Orbits
Erman Cineli, Viktor L. Ginzburg, Basak Z. Gurel +1
We investigate the effect of a hyperbolic (or, more generally, isolated as an invariant set) closed Reeb orbit on the dynamics of a Reeb flow on the -dimensional standard c…