Related papers: Wild dynamics on manifolds
Variational formulations of statics and dynamics of mechanical systems controlled by external forces are presented as examples of variational principles.
In this paper, we treat symplectic difference equations with one degree of freedom. For such cases, we resolve the relation between that the dynamics on the two dimensional phase space is reduced to on one dimensional level sets by a…
A review of some recent results and ideas about the expected behaviour of large chaotic systems and fluids.
We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…
This article deals with invariant manifolds for infinite dimensional random dynamical systems with different time scales. Such a random system is generated by a coupled system of fast-slow stochastic evolutionary equations. Under suitable…
We develop a tool in order to analyse the dynamics of differentiable flows with singularities. It provides an abstract model for the local dynamics that can be used in order to control the size of invariant manifolds. This work is the first…
The notion of a holomorphically symplectic manifold can be generalized to the singular one. This paper studies the birational contraction maps between symplectic varieties, and then describes the deformation of a symplectic variety which…
The singular bifurcations in a dispersive billiard are discussed in terms of symbolic dynamics and is compared to an example of a bifurcation tree in a smooth potential. Possible generalizations to other smooth potentials are discussed.
Topological dynamics constitutes the study of asymptotic properties of orbits under flows or maps on the Hausdorff phase space. Hyperbolic dynamics is the study of differentiable flows or maps that are usually characterized by the presence…
Constructible complexes have the same characteristic cycle if they have the same wild ramification, even if the characteristics of the coefficients fields are different.
We consider motion in a periodic potential in a classical, quantum, and semiclassical context. Various results on the distribution of asymptotic velocities are proven.
We present some constructions that are merely the fruit of combining recent results from two areas of smooth dynamics: nonuniformly hyperbolic systems and elliptic constructions.
Several geometric flows on symplectic manifolds are introduced which are potentially of interest in symplectic geometry and topology. They are motivated by the Type IIA flow and T-duality between flows in symplectic geometry and flows in…
We classify the periodic Hamiltonian flows on compact four dimensional symplectic manifolds up to isomorphism of Hamiltonian S^1 spaces. Additionally, we show that all these spaces are Kaehler, that every such space is obtained from a…
The coeffective differential complex on a symplectic manifold is extended both in length and in scope, unifying the constructions of various other authors.
A discrete model of traffic on a multilane road is considered. The traffic is presented as particles movement with a deterministic component and a stochastic one. Formulas for the traffic characteristics have been found. The model can…
In this paper we study kinematic expansive flows on compact metric spaces, surfaces and general manifolds. Different variations of the definition are considered and its relationship with expansiveness in the sense of Bowen-Walters and…
We give an example of a symplectic manifold with a stable hypersurface such that nearby hypersurfaces are typically unstable.
Recent experimental results on directed and elliptic flow, theoretical developments, and new techniques for anisotropic flow analysis are reviewed.
These are notes to accompany my lectures at the $2024$ "Current Developments in Mathematics" conference hosted by Harvard/MIT. The lectures were about some recent progress in our understanding of two and three dimensional dynamical systems,…