Infinitesimal symmetries in contact Hamiltonian systems

Symmetries and singularities in Hamiltonian systems

This paper contains several results concerning the role of symmetries and singularities in the mathematical formulation of many physical systems. We concentrate in systems which find their mathematical model on a symplectic or Poisson manifold and we present old and new results from a global perspective.

Infinite Dimensional Hamiltonian Systems with Symmetries

We give a survey of infinite dimensional Hamiltonian systems with infinite dimensional Lie groups as symmetry groups and discuss concrete examples from soliton equations, plasma physics, fluid mechanics and quantum field theory. We present some new results of applications to BRST symmetries and g-symplectic structures.

Average-preserving symmetries and energy equipartition in linear Hamiltonian systems

This paper analyzes energy equipartition in linear Hamiltonian systems in a deterministic setting.We consider the group of phase space symmetries of a stable linear Hamiltonian system, and characterize the subgroup of symmetries whose elements preserve the time averages of quadratic functions along the trajectories of the system. As a corollary, we show that if the system has simple eigenvalues...

Symmetries of Hamiltonian systems on symplectic and Poisson manifolds

SYMMETRIES OF PDEs SYSTEMS IN SOLAR PHYSICS AND CONTACT GEOMETRY

One considers a class of PDEs systems (1) equivalent to (8) and one determines the PDEs system (10) which defines the associated symmetry group. Particularly, for the Blair system (2)+(3) equivalent to (14), one finds the symmetry Lie group G (Theorem 5). One proves that the class of PDEs systems in the form (8)+(14′) which are invariant with respect to the Lie group G, is reduced to the Blair ...