6 citations · 16 across the 9 of their papers we have counts for
9 papers
Remarks on the systoles of symmetric convex hypersurfaces and symplectic capacities
Joontae Kim, Seongchan Kim, Myeonggi Kwon
In this note we study the systoles of convex hypersurfaces in invariant under an anti-symplectic involution. We investigate a uniform upper bound of the ratio bet…
Symmetric periodic orbits and invariant disk-like global surfaces of section on the three-sphere
Seongchan Kim
We study Reeb dynamics on the three-sphere equipped with a tight contact form and an anti-contact involution. We prove the existence of a symmetric periodic orbit and provide neces…
Bifurcations of symmetric periodic orbits via Floer homology
Joontae Kim, Seongchan Kim, Myeonggi Kwon
We give criteria for the existence of bifurcations of symmetric periodic orbits in reversible Hamiltonian systems in terms of local equivariant Lagrangian Rabinowitz Floer homology…
Equivariant wrapped Floer homology and symmetric periodic Reeb orbits
Joontae Kim, Seongchan Kim, Myeonggi Kwon
The aim of this article is to apply a Floer theory to study symmetric periodic Reeb orbits. We define positive equivariant wrapped Floer homology using a (anti-)symplectic involuti…
On families of periodic orbits in the restricted three-body problem
Seongchan Kim
Since Poincaré, periodic orbits have been one of the most important objects in dynamical systems. However, searching them is in general quite difficult. A common way to find them i…
-like invariants of periodic orbits of the second kind in the restricted three body problem
Joontae Kim, Seongchan Kim
We determine three invariants: Arnold's -invariant as well as and invariants, which were introduced by Cieliebak-Frauenfelder-van Koert, of per…
On a convex embedding of the Euler problem of two fixed centers
Seongchan Kim
In this article, we study a convex embedding for the Euler problem of two fixed centers for energies below the critical energy level. We prove that the doubly-covered elliptic coor…
Homoclinic orbits in the Euler problem of two fixed centers
Seongchan Kim
We give a complete description of the shapes and the behavior of all homoclinic orbits in the Euler problem of two fixed centers.
Dynamical convexity of the Euler problem of two fixed centers
Seongchan Kim
We give thorough analysis for the rotation functions of the critical orbits from which one can understand bifurcations of periodic orbits. Moreover, we give explicit formulas of th…