Related papers: Action selectors and Maslov class rigidity

For many classes of symplectic manifolds, the Hamiltonian flow of a function with sufficiently large variation must have a fast periodic orbit. This principle is the base of the notion of Hofer-Zehnder capacity and some other symplectic…

We discuss symplectic manifolds where, locally, the structure is that encountered in Lagrangian dynamics. Exemples and characteristic properties are given. Then, we refer to the computation of the Maslov classes of a Lagrangian submanifold.…

We introduce action-driven flows for causal variational principles, being a class of non-convex variational problems emanating from applications in fundamental physics. In the compact setting, H\"older continuous curves of measures are…

In this paper we introduce invariants of semi-free Hamiltonian actions of $S\sp 1$ on compact symplectic manifolds (which satisfy some technical conditions related to positivity) using the space of solutions to certain gauge theoretical…

We study the action functional associated to a smooth Lagrangian function on the cotangent bundle of a manifold, having quadratic growth in the velocities. We show that, although the action functional is in general not twice differentiable…

The purpose of this article is to characterize symplectic and Hamiltonian circle actions on symplectic manifolds in terms of symplectic embeddings of Riemann surfaces. More precisely, we will show that (1) if $(M,\omega)$ admits a…

The main result of this paper is a construction of finitely additive measures for higher rank abelian actions on Heisenberg nilmanifolds. Under a full measure set of Diophantine conditions for the generators of the action, we construct…

We study the action of Hamiltonian diffeomorphisms of a compact symplectic manifold ($X,\omega$) on $C^\infty(X)$ and on functions $C^\infty(X)\to \mathbb R$. We describe various properties of invariant convex functions on $C^\infty(X)$.…

We consider open symplectic manifolds which admit dilations (in the sense previously introduced by Solomon and the author). We obtain restrictions on collections of Lagrangian submanifolds which are pairwise disjoint (or pairwise…

We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar…

In this paper we first show that the necessary condition introduced in our previous paper is also a sufficient condition for a path to be a geodesic in the group $\Ham^c(M)$ of compactly supported Hamiltonian symplectomorphisms. This…

In the present paper we introduce the notion of complex asystatic Hamiltonian action on a K\"ahler manifold. In the algebraic setting we prove that if a complex linear group $G$ acts complex asystatically on a K\"ahler manifold then the…

Let $(M,\omega)$ be a Hamiltonian $G$-space with a momentum map $F:M \to {\frak g}^*$. It is well-known that if $\alpha$ is a regular value of $F$ and $G$ acts freely and properly on the level set $F^{-1}(G\cdot \alpha)$, then the reduced…

In this paper, we prove that the two well-known natural normalizations of Hamiltonian functions on the symplectic manifold $(M,\omega)$ canonically relates the action spectra of different normalized Hamiltonians on {\it arbitrary}…

We construct finite group actions on Lagrangian Floer theory when symplectic manifolds have finite group actions and Lagrangian submanifolds have induced group actions. We first define finite group actions on Novikov-Morse theory. We…

Let $L$ be the sublaplacian and $T$ the partial Laplacian with respect to central variables on H-type groups. We investigate a class of invariant differential operators by the joint functional calculus of $L$ and $T$. We establish…

Let $(M,\omega)$ be a ruled symplectic four-manifold. If $(M, \omega)$ is rational, then every homologically trivial symplectic cyclic action on $(M,\omega)$ is the restriction of a Hamiltonian circle action.

Let $M$ be a closed Fano symplectic manifold with a semifree Hamiltonian circle action with isolated maximum. We compute the Gromov width and the Hofer-Zehnder capacity of $M$ using a moment map.

In this paper we generalize constructions of non-commutative integrable systems to the context of weakly Hamiltonian actions on Poisson manifolds. In particular we prove that abelian weakly Hamiltonian actions on symplectic manifolds split…

Multiplicity results for solutions of various boundary value problems are known for dynamical systems on compact configuration manifolds, given by Lagrangians or Hamiltonians which have quadratic growth in the velocities or in the momenta.…