Jungsoo Kang

In this paper, we prove that a dynamically convex starshaped hypersurface in <f>$\\mathbb {C}^2$</f> which is invariant under complex conjugation admits a global surface of section which is invariant under conjugation as well. We obtain this invariant global surface by embedding <f>$\\mathbb {C}^2$</f> into <f>$\\mathbb {CP}^2$</f> and applying a stretching argument to real holomorphic curves in <f>$\\mathbb {CP}^2$</f>. The motivation for this res

In this paper, we extend Rabinowitz Floer homology theory which has been established and extensively studied for hypersurfaces to coisotropic submanifolds of higher codimension.With this generalized version of Rabinowitz Floer homology theory, we explore the coisotropic intersection problem which interpolates between the Lagrangian intersection problem and the closed orbit problem.To be specific, we study the existence of leafwise intersection points on contact coisotropic submanifolds and the d

We study the existence of multiple closed Reeb orbits on some contact manifolds by means of S 1 -equivariant symplectic homology and the index iteration formula. We prove that a certain class of contact manifolds which admits displaceable exact contact embeddings, a certain class of prequantization bundles, and Brieskorn spheres have multiple closed Reeb orbits.

In this article, we study the question of existence of leafwise intersection points for contact manifolds which are not necessarily of restricted contact type. Moreover we can find a leafwise intersection point on the symplectization for special Hamiltonian functions.

In this paper, we extend Rabinowitz Floer homology theory which has been established and extensively studied for hypersurfaces to coisotropic submanifolds of higher codimension. With this generalized version of Rabinowitz Floer homology theory, we explore the coisotropic intersection problem which interpolates between the Lagrangian intersection problem and the closed orbit problem. To be specific, we study the existence of leafwise intersection points on contact coisotropic submanifolds and the

In reversible dynamical systems, it is of great importance to understand symmetric features. The aim of this paper is to explore symmetric periodic points of reversible maps on planar domains invariant under a reflection. We extend Franks’ theorem on a dichotomy of the number of periodic points of area-preserving maps on the annulus to symmetric periodic points of area-preserving reversible maps. Interestingly, even a non-symmetric periodic point guarantees infinitely many symmetric periodic poi

In this paper, we show that if Rabinowitz Floer homology has infinitedimension, there exist infinitely many critical points of a Rabinowitz actionfunctional even though it could be non-Morse. This result is proved byexamining filtered Rabinowitz Floer homology.

In reversible dynamical systems, it is frequently of importance to understand symmetric features. The aim of this paper is to explore symmetric periodic points of reversible maps on planar domains invariant under a reflection. We extend Franks' theorem on a dichotomy of the number of periodic points of area preserving maps on the annulus to symmetric periodic points of area preserving reversible maps. Interestingly, even a non-symmetric periodic point guarantees infinitely many symmetric periodi

The planar circular restricted three-body problem (PCRTBP) is symmetric with respect to the line of masses and there is a corresponding anti-symplectic involution on the cotangent bundle of the 2-sphere in the regularized PCRTBP. Recently it turned out that each bounded component of an energy hypersurface with low energy for the regularized PCRTBP is fiberwise starshaped. This enables us to define a Lagrangian Rabinowitz Floer homology which is related to periodic orbits symmetric for the anti-s

In this article, we focus on the invariance property of Morse homology on noncompact manifolds. We expect to apply outcomes of this article to several types of Floer homology, thus we define Morse homology purely axiomatically and algebraically. The Morse homology on noncompact manifolds generally depends on the choice of Morse functions; it is easy to see that critical points may escape along homotopies of Morse functions on noncompact manifolds. Even worse, homology classes also can escape alo

We study the existence of multiple closed Reeb orbits on some contact manifolds by means of $S^1$-equivariant symplectic homology and the index iteration formula. It is proved that a certain class of contact manifolds which admit displaceable exact contact embeddings, a certain class of prequantization bundles, and Brieskorn spheres have multiple closed Reeb orbits.

Rabinowitz Floer homology has been investigated on a submanifold of contact type. The contact condition, however, is quite restrictive. For example, a product of contact hypersurfaces is rarely of contact type. In this article, we study Rabinowitz Floer homology for a class of non-contact submanifolds. We show for this example that there are infinitely many leafwise intersection points by proving a Künneth formula for Rabinowitz Floer homology.