A generalised Hopf algebra for solitons.
A generalization for Peakon's solitary wave and Camassa-Holm equation.
A generalization of semiflows on monomials
Let be a field, and the set of monomials of . It is well known that the set of monomial ideals of is in a bijective correspondence with the set of all subsemiflows of the -semiflow . We generalize this to the case of term ideals of , where is a commutative Noetherian ring. A term ideal of is an ideal of generated by a family of terms , where and are integers .
A generalization of Straube's theorem: existence of absolutely continuous invariant measures for random maps.
A generalization of the self-dual induction to every interval exchange transformation
We generalize to all interval exchanges the induction algorithm defined by Ferenczi and Zamboni for a particular class. Each interval exchange corresponds to an infinite path in a graph whose vertices are certain unions of trees we call castle forests. We use it to describe those words obtained by coding trajectories and give an explicit representation of the system by Rokhlin towers. As an application, we build the first known example of a weakly mixing interval exchange outside the hyperelliptic...
A generalization of the Weinstein-Moser theorems on periodic orbits of a hamiltonian system near an equilibrium
A gentle (without chopping) approach to the full Kostant-Toda lattice.
A geometric analysis of dynamical systems with singular Lagrangians
We study dynamics of singular Lagrangian systems described by implicit differential equations from a geometric point of view using the exterior differential systems approach. We analyze a concrete Lagrangian previously studied by other authors by methods of Dirac’s constraint theory, and find its complete dynamics.
A geometric approach to a result of Benci and Giannoni for Hamiltonian systems with singular potentials.
A geometric approach to invariant sets for dynamical systems.
A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field, using a Fock space approach
In this article the linear Boltzmann equation is derived for a particle interacting with a Gaussian random field, in the weak coupling limit, with renewal in time of the random field. The initial data can be chosen arbitrarily. The proof is geometric and involves coherent states and semi-classical calculus.
A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: announcement of results.
A geometric setting for classical molecular dynamics
A global analysis of Newton iterations for determining turning points
The global convergence of a direct method for determining turning (limit) points of a parameter-dependent mapping is analysed. It is assumed that the relevant extended system has a singular root for a special parameter value. The singular root is clasified as a (i.e., as a turning point). Then, the Theorz for Imperfect Bifurcation offers a particular scenario for the split of the singular root into a finite number of regular roots (turning points) due to a given parameter imperfection. The relationship...
A global factorization theorem for the ZS-AKNS system.
A global perspective for non-conservative dynamics
A gradient inequality at infinity for tame functions.
Let f be a C1 function defined over Rn and definable in a given o-minimal structure M expanding the real field. We prove here a gradient-like inequality at infinity in a neighborhood of an asymptotic critical value c. When f is C2 we use this inequality to discuss the trivialization by the gradient flow of f in a neighborhood of a regular asymptotic critical level.
A graph approach to computing nondeterminacy in substitutional dynamical systems
We present an algorithm which for any aperiodic and primitive substitution outputs a finite representation of each special word in the shift space associated to that substitution, and determines when such representations are equivalent under orbit and shift tail equivalence. The algorithm has been implemented and applied in the study of certain new invariants for flow equivalence of substitutional dynamical systems.
A holomorphic correspondence at the boundary of the Klein combination locus
We investigate an explicit holomorphic correspondence on the Riemann sphere with striking dynamical behaviour: the limit set is a fractal resembling the one-skeleton of a tetrahedron and on each component of the complement of this set the correspondence behaves like a Fuchsian group.
A Hopf bifurcation of interfaces in a Dirichlet problem.