Specific Features of Families of Invariant Manifolds of Conservative Systems

On the Peculiar Properties of Families of Invariant Manifolds of Conservative Systems

Statistical cosymplectic manifolds and their submanifolds

    In ‎this ‎paper‎, we introduce statistical cosymplectic manifolds and investigate some properties of their tensors. We define invariant and anti-invariant submanifolds and study invariant submanifolds with normal and tangent structure vector fields. We prove that an invariant submanifold of a statistical cosymplectic manifold with tangent structure vector field is a cosymplectic and minimal...

On Invariant Manifolds of Nonholonomic Systems

Invariant manifolds of equations governing the dynamics of conservative nonholonomic systems are investigated. These manifolds are assumed to be uniquely projected onto configuration space. The invariance conditions are represented in the form of generalized Lamb’s equations. Conditions are found under which the solutions to these equations admit a hydrodynamical description typical of Hamilton...

Invariant manifolds and global bifurcations.

Invariant manifolds are key objects in describing how trajectories partition the phase spaces of a dynamical system. Examples include stable, unstable, and center manifolds of equilibria and periodic orbits, quasiperiodic invariant tori, and slow manifolds of systems with multiple timescales. Changes in these objects and their intersections with variation of system parameters give rise to globa...

Transverse intersection of invariant manifolds in perturbed multi-symplectic systems

A multi-symplectic system is a PDE with a Hamiltonian structure in both temporal and spatial variables. This paper considers spatially periodic perturbations of symmetric multi-symplectic systems. Due their structure, unperturbed multi-symplectic systems often have families of solitary waves or front solutions, which together with the additional symmetries lead to large invariant manifolds. Per...