arXiv subjects

Beomjun Sohn

Publications and source records attributed to Beomjun Sohn.

3 recordsLinked to original sources

arXiv2026

Robustness of topological entropy under small area deformations

In this paper, we establish a new type of stability phenomenon for the topological entropy of Hamiltonian diffeomorphisms of closed surfaces. For a closed surface endowed with an area form $(\Sigma,\omega)$ and a Hamiltonian diffeomorphism $\phi$ of $(\Sigma,\omega)$, we show that for every $\varepsilon>0$ there exists $A=A(\phi,\varepsilon)>0$ such that \[ h_{\mathrm{top}}(\phi') > h_{\mathrm{top}}(\phi)-\varepsilon \] for every Hamiltonian diffeomorphism $\phi'$ obtained from $\phi$ by a deformation supported in a disjoint union of disks, each of area less than $A$. In particular, if $h_{\mathrm{top}}(\phi)>0$, then $\phi$ cannot be made to have zero entropy by an area-preserving deformation supported in disks of small area. This follows from the new braid stability result established in this paper with respect to the spectral distance recently introduced by Connery-Grigg.

math.SG↗

arXiv2026

Hofer-Zehnder capacity as a geodesic selector

We compute the Hofer-Zehnder capacity of the unit disk cotangent bundle of every ellipsoid in $\mathbb R^3$. The capacity is determined by the smaller of two distinguished quantities in the geodesic length spectrum: twice the systole and the length of the shortest simple closed geodesic of Morse index 3. For the lower bound, we use Riemannian billiards on a suitable cut of the ellipsoid. For the upper bounds, we develop two complementary methods. The first combines an argument by Hofer-Viterbo with neck-stretching and yields, more generally, an upper bound for positively curved Riemannian two-spheres in terms of closed geodesics of prescribed index. The second uses the pair-of-pants product in symplectic homology and the Viterbo isomorphism to bound the Hofer-Zehnder capacity of any disk cotangent bundles of Riemannian two-spheres by twice the diastole; for positive curvature, the diastole agrees with the systole.

math.SG↗

arXiv2023

Barcode entropy for Reeb flows on contact manifolds with Liouville fillings

We study the topological entropy of Reeb flows on contact manifolds with Liouville fillings. With the theory of persistence modules, we define SH-barcode entropy from the symplectic homology of a filling. We prove that the SH-barcode entropy is independent of the choice of the filling and that the barcode entropy provides a lower bound for the topological entropy of the Reeb flow.

math.SG↗