Related papers: Wild dynamics on manifolds
The aim of this paper is to study dynamical and topological properties of a flow in the region of influence of an isolated non-saddle set or a $W$-set in a manifold. These are certain classes of compact invariant sets in whose vicinity the…
Dynamical models underpin our ability to understand and predict the behavior of natural systems. Whether dynamical models are developed from first-principles derivations or from observational data, they are predicated on our choice of state…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
Statistical properties of evolving random graphs are analyzed using kinetic theory. Treating the linking process dynamically, structural characteristics such as links, paths, cycles, and components are obtained analytically using the rate…
This manuscript contains nothing new, but synthesizes known results: For the theoretical population geneticist with a probabilistic background, we provide a summary of some key results on stochastic differential equations. For the…
We present several variants of the Maupertuis principle, both on the exact and the non exact symplectic manifolds.
We present several methods for predicting the dynamics of Hamiltonian systems from discrete observations of their vector field. Each method is either informed or uninformed of the Hamiltonian property. We empirically and comparatively…
We recall the notion of a differential operator over a smooth map (in linear and non-linear settings) and consider its versions such as formal $\hbar$-differential operators over a map. We study constructions and examples of such operators,…
We study analysis over infinite dimensional manifolds consisted by sequences of almost K\"ahler manifolds. In particular we develop moduli theory of pseudo holomorphic curves into the spaces with high symmetry. As applications, we study…
The past few years have seen many advances in our understanding of the dynamics of polymeric fluids. These include improvements on the successful reptation theory; an emerging molecular theory of semiflexible chain dynamics; and an…
The dynamical behavior caused by dry friction is studied for a spring-block system pulled with constant velocity over a surface. The dynamical consequences of a general type of phenomenological friction law (stick-time dependent static…
We present here the concept of Dominated Splitting and give an account of some important results on its dynamics.
We analyze a variety of Weyl invariant dynamical problems in three dimensions.
It is proved that the tame automorphism group of a differential polynomial algebra $k\{x,y\}$ over a field $k$ of characteristic $0$ in two variables $x,y$ with $m$ commuting derivations $\delta_1, \ldots, \delta_m$ is a free product with…
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 investigate the uniqueness of so-called exotic structures on certain exact symplectic manifolds by looking at how their symplectic properties change under small nonexact deformations of the symplectic form. This allows us to distinguish…
This paper uses a generalization of symplectic geometry, known as $n$-symplectic geometry and developed by Norris, to find observables on three-dimensional manifolds. It will be seen that for the cases considered, the $n$-symplectic…
The convenient setting for smooth mappings, holomorphic mappings, and real analytic mappings in infinite dimension is sketched. Infinite dimensional manifolds are discussed with special emphasis on smooth partitions of unity and tangent…
We numerically investigate the orbital dynamics of a two-dimensional galactic model, emphasizing the influence of stable and unstable manifolds on the evolution of orbits. In our analysis we use evaluations of the system's Lagrangian…
Sheaf theoretically based Abstract Differential Geometry incorporates and generalizes all the classical differential geometry. Here, we undertake to partially explore the implications of Abstract Differential Geometry to classical…