Related papers: Totally Non-coisotropic Displacement and Its Appli…
We address the following problem: if a Hamiltonian diffeomorphism maps a Lagrangian submanifold $L$ to a small Weinstein neighborhood of $L$, is the image necessarily Hamiltonian isotopic to $L$ inside that neighborhood? On the one hand, we…
We prove that for every compact K\"ahler manifold $X$ there exists an $L$-infinity morphism, lifting the usual cup product in cohomology, from the Kodaira-Spencer differential graded Lie algebra to the suspension of the space of linear…
We develop an isotopy principle for holomorphic motions. Our main result concerns the extendability of a holomorphic motion of a finite subset $E$ of a Riemann surface $Y$ parameterized by a point $t$ in a pointed hyperbolic surface $(X,…
We consider the spectral action within the context of a 4-dimensional manifold with torsion and show that, in the vacuum case, the equations of motion reduce to Einstein's equations, securing the linear stability of the theory. To…
We study Hamiltonian diffeomorphisms of closed symplectic manifolds with non-contractible periodic orbits. In a variety of settings, we show that the presence of one non-contractible periodic orbit of a Hamiltonian diffeomorphism of a…
The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the…
We obtain estimates showing that on monotone symplectic manifolds (asymptotic) spectral invariants of Hamiltonians which vanish on a non-empty open set, U, descend to Ham_c(M\setminus U) from its universal cover. Furthermore, we show these…
We prove a $C^\infty$ closing lemma for Hamiltonian diffeomorphisms of closed surfaces. This is a consequence of a $C^\infty$ closing lemma for Reeb flows on closed contact three-manifolds, which was recently proved as an application of…
The main purpose of this paper is to study the length minimizing property of Hamiltonian paths on closed symplectic manifolds $(M,\omega)$ such that there are no spherical homology class $A \in H_2(M)$ with $$ \omega(A) > 0 \quad \text{and}…
Adding small random parametric noise to an arc of diffeomophisms of a manifold of dimension 3, generically unfolding a codimension one quadratic homoclinic tangency q associated to a sectionally dissipative saddle fixed point p, we obtain…
It is shown that the geometry of locally homogeneous multisymplectic manifolds (that is, smooth manifolds equipped with a closed nondegenerate form of degree > 1, which is locally homogeneous of degree k with respect to a local Euler field)…
We investigate the geometric and topological properties of the group of locally conformally symplectic (LCS) diffeomorphisms, utilizing the LCS flux homomorphism defined by S. Haller. By analyzing the flux map from the universal cover of…
The main theme of the paper is the dynamics of Hamiltonian diffeomorphisms of ${\mathbb C}{\mathbb P}^n$ with the minimal possible number of periodic points (equal to $n+1$ by Arnold's conjecture), called here Hamiltonian pseudo-rotations.…
We prove Wadsley's theorem for foliations by closed non-lightlike geodesics. As an application we show that every pseudo-Riemannian and non-Riemannian 2-mainfold, all of whose time- or spacelike geodesics are closed, is diffeomorphic to…
We prove a theorem that generalizes Schmidt's Subspace Theorem in the context of metric diophantine approximation. To do so we reformulate the Subspace theorem in the framework of homogeneous dynamics by introducing and studying a slope…
We prove that a $C^0$--small area preserving homeomorphism of a closed surface with vanishing mass flow can not displace a topological disk of large area. This resolves the displaced disks problem posed by F. B\'eguin, S. Crovisier, and F.…
We study Hamiltonian diffeomorphisms on symplectic Euclidean spaces that are equal to non-degenerate linear maps at infinity. Under the assumption that there exists an isolated homologically nontrivial fixed point satisfying the twist…
We show the existence of a local stable manifold for a bidirectional discrete-time nondiffeomorphic nonlinear Hamiltonian dynamics. This is the case where zero is a closed loop eigenvalue and therefore the Hamiltonian matrix is not…
In this paper we prove that if $f$ is a self-mapping of a nonempty subset $K$ of a normed space $X$ that satisfies some mild conditions, then the minimal displacement of large iterations $f^n$ always dominates that of $f$ along certain…
We establish the leafwise intersection property for closed, coisotropic submanifolds in an exact symplectic manifold satisfying natural additional assumptions.