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For a positive integer n and R>0, we set
. Given R>1 and n≥4 we construct a sequence of analytic perturbations (H j) of the completely integrable Hamiltonian
on
, with unstable orbits for which we can estimate the time of drift in the action space. These functions H j are analytic on a fixed complex neighborhood V of
, and setting
the time of drift of these orbits is smaller than (C(1/ɛ j)1/2(n-3)) for a fixed constant c>0. Our unstable orbits stay close to a doubly resonant surface,...
The purpose of this paper is to establish a connection between various objects such as
dynamical -matrices, Lie bialgebroids, and Lagrangian subalgebras. Our method relies
on the theory of Dirac structures and Courant algebroids. In particular, we give a new
method of classifying dynamical -matrices of simple Lie algebras , and
prove that dynamical -matrices are in one-one correspondence with certain Lagrangian
subalgebras of .
A discrete time stochastic model for a multiagent system given in terms of a large collection of interacting Markov chains is studied. The evolution of the interacting particles is described through a time inhomogeneous transition probability kernel that depends on the ‘gradient’ of the potential field. The particles, in turn, dynamically modify the potential field through their cumulative input. Interacting Markov processes of the above form have been suggested as models for active biological transport...
In this paper we develop the distinguished (d-) Riemannian differential geometry (in the sense of d-connections, d-torsions, d-curvatures and some geometrical Maxwell-like and Einstein-like equations) for the polymomentum Hamiltonian which governs the multi-time electrodynamics.
We define the divergence operators on a graded algebra, and we show that, given an odd
Poisson bracket on the algebra, the operator that maps an element to the divergence of
the hamiltonian derivation that it defines is a generator of the bracket. This is the
“odd laplacian”, , of Batalin-Vilkovisky quantization. We then study the
generators of odd Poisson brackets on supermanifolds, where divergences of graded vector
fields can be defined either in terms of berezinian volumes or of graded connections.
Examples...
It is shown how to extend the formal variational calculus in order to incorporate integrals of divergences into it. Such a generalization permits to study nontrivial boundary problems in field theory on the base of canonical formalism.
We consider Lagrangian systems with Lagrange functions which exhibit a quadratic time dependence. We prove the existence of infinitely many solutions tending, as , to an «equilibrium at infinity». This result is applied to the Kirchhoff problem of a heavy rigid body moving through a boundless incompressible ideal fluid, which is at rest at infinity and has zero vorticity.
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