Related papers: Wild dynamics on manifolds
In this article, we generalize the theory of discrete Lagrangian mechanics and variational integrators in two principal directions. First, we show that Lagrangian submanifolds of symplectic groupoids give rise to discrete dynamical systems,…
A coupled map lattice whose topology changes at each time step is studied. We show that the transversal dynamics of the synchronization manifold can be analyzed by the introduction of effective dynamical quantities. These quantities are…
We prove some properties of analytic multiplicative and sub-multiplicative cocycles. The results allow to construct natural invariant analytic sets associated to complex dynamical systems.
This is an expository paper on the dynamical properties of substitutions in propositional many-valued logics. We identify substitutions with endomorphisms of free algebras, and we study their actions on the dual spectral spaces.
Simple random walks on various types of partially horizontally oriented regular lattices are considered. The horizontal orientations of the lattices can be of various types (deterministic or random) and depending on the nature of the…
In this work we construct a variety of new complex-valued proper biharmonic maps and (2,1)-harmonic morphisms on Riemannian manifolds with non-trivial geometry. These are solutions to a non-linear system of partial differential equations…
We study the classical motion in bidimensional polygonal billiards on the sphere. In particular we investigate the dynamics in tiling and generic rational and irrational equilateral triangles. Unlike the plane or the negative curvature…
The difference variational bicomplex, which is the natural setting for systems of difference equations, is constructed and used to examine the geometric and algebraic properties of various systems. Exactness of the bicomplex gives a…
Dynamical sampling refers to a class of problems in which space-time samples are taken from a signal evolving under an underlying dynamical system. The goal is to use these samples to recover relevant information about the system, such as…
Let a finite set of interacting particles be given, together with a symmetry Lie group $G$. Here we describe all possible dynamics that are jointly equivariant with respect to the action of $G$. This is relevant e.g., when one aims to…
We develop an theoretical approach for predicting biodiversity in multi-dimensional niche spaces, arising due to ecological drivers such as competitive exclusion. The novelty of our approach relies on the fact that ecological niches are…
We investigate orthogonal and symplectic bundles with parabolic structure, over a curve.
The main purpose of this paper is to show the existence of action-angle variables for integrable Hamiltonian systems on Dirac manifolds under some natural regularity and compactness conditions, using the torus action approach. We show that…
Exterior differential forms with values in the (Kostant's) symplectic spinor bundle on a manifold with a given metaplectic structure are decomposed into invariant subspaces. Projections to these invariant subspaces of a covariant derivative…
We discuss the interplay between the piece-line regular and vertex-angle singular boundary effects, related to integrability and chaotic features in rational polygonal billiards. The approach to controversial issue of regular and irregular…
Homoclinic bifurcation of 4-dimensional symplectic mappings is asymptotically studied. We construct the 2-dimensional stable and unstable manifolds near the sub-manifolds which experience exponentially small splitting, and successfully…
We give an overview of various recent results concerning the topology of symplectic 4-manifolds and singular plane curves, using branched covers and isotopy problems as a unifying theme. While this paper does not contain any new results, we…
The geography of minimal symplectic 4-manifolds with arbitrary fundamental group and symplectic 6-manifolds with abelian fundamental group of small rank, and with arbitrary fundamental group are addressed.
We have researched the condition for symplectic discretization to preserve local boundedness for the space of 2-dimensional Hamiltonian dynamical systems in this paper.
In this paper we combine two powerful computational techniques, well-tempered metadynamics and time lagged independent component analysis. The aim is to develop a new tool for studying rare events and exploring complex free energy…