Related papers: Wild dynamics on manifolds
On a symplectic manifold a family of generalized Poisson brackets associated with powers of the symplectic form is studied. The extreme cases are related to the Hamiltonian and Liouville dynamics. It is shown that the Dirac brackets can be…
Examples of nonformal simply connected symplectic manifolds are constructed.
In this note, we extend to the singular case some results on the birational geometry of irreducible holomorphic symplectic manifolds.
New types of maximal symplectic partial spreads are constructed.
The study of algebraic properties of groups of transformations of a manifold gives rise to an interplay between different areas of mathemathics such as topology, geometry, and dynamical systems. Especially, in this paper, we point out some…
We mostly determine which closed smooth oriented 4-manifolds fibering over lower dimensional manifolds are virtually symplectic, i.e. finitely covered by symplectic 4-manifolds.
In this paper we relate the study of actions of discrete groups over connected manifolds to that of their orbit spaces seen as differentiable stacks. We show that the orbit stack of a discrete dynamical system on a simply connected manifold…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
In this article we study multisymplectic geometry, i.e., the geometry of manifolds with a non-degenerate, closed differential form. First we describe the transition from Lagrangian to Hamiltonian classical field theories, and then we…
A list of open problems on holomorphic symplectic, contact and Poisson manifolds.
A variational model of pressure-dependent plasticity employing a time-incremental setting is introduced. A novel formulation of the dissipation potential allows one to construct the condensed energy in a variationally consistent manner. For…
We discuss some examples in which symplectic monodromy (provably or conjecturally) splits off the symplectic mapping class group, hoping to illustrate different techniques and inputs to the arguments. Along the way we formulate several open…
We present the Hamiltonian formalism for the Euler equation of symplectic fluids, introduce symplectic vorticity, and study related invariants. In particular, this allows one to extend D.Ebin's long-time existence result for geodesics on…
We study moduli spaces of meromorphic connections (with arbitrary order poles) over Riemann surfaces together with the corresponding spaces of monodromy data (involving Stokes matrices). Natural symplectic structures are found and described…
This is a very biased and incomplete survey of some basic notions, old and new results, as well as open problems concerning Weinstein symplectic manifolds.
The study of the structure of translational tilings has captivated mathematicians, scientists, and the general public for centuries and continues to thrive at the crossroads of analysis, combinatorics, dynamics, logic, number theory, and…
We present a brief survey of the spectral theory and dynamics of infinite volume asymptotically hyperbolic manifolds. Beginning with their geometry and examples, we proceed to their spectral and scattering theories, dynamics, and the…
The billiard problem of statistical physics is considered in a new geometric approach with a symmetric phase space. The structure and topological features of typical billiard phase portrait are defined. The connection between geometric,…
The modern qualitative theory of dynamical systems is thoroughly intertwined with the fairly young science of topology. Strange and even bizarre constructions of topology are found sooner or later in dynamics of discrete or continuous…
With the help of molecular dynamics simulations we study an ensemble of active dumbbells in purely repulsive interaction. We derive the phase diagram in the density-activity plane and we characterise the various phases with liquid, hexatic…