8 citations · 24 across the 14 of their papers we have counts for
18 papers
Filtered Symplectic Homology and Closed Reeb Orbits
Erman Cineli, Viktor L. Ginzburg, Basak Z. Gurel
We further explore connections between the symplectic homology persistence module and the properties of closed Reeb orbits for star-shaped domains in higher dimensions. Our first r…
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…
From Barcode Entropy to Metric Entropy
Erman Cineli, Viktor L. Ginzburg, Basak Z. Gurel
We establish a connection between barcode entropy and metric entropy. Namely, we show that the barcode entropy bounds the metric entropy from below for a measure from a specific cl…
Ergodic closing lemmas and invariant Lagrangians
Erman Cineli, Sobhan Seyfaddini, Shira Tanny
Motivated by the ergodic closing lemma of Mañé, we investigate the closing lemma in higher-dimensional Hamiltonian systems, with a focus on the statistical behavior of p…
Closed Orbits of Dynamically Convex Reeb Flows: Towards the HZ- and Multiplicity Conjectures
Erman Cineli, Viktor L. Ginzburg, Basak Z. Gurel
We study the multiplicity problem for prime closed orbits of dynamically convex Reeb flows on the boundary of a star-shaped domain in . The first of our two main r…
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…