Nonautonomous fractional Hamiltonian system with critical exponential growth

Anomalous fluctuations for a perturbed hamiltonian system with exponential interactions

A one-dimensional Hamiltonian system with exponential interactions perturbed by a conservative noise is considered. It is proved that energy superdiffuses and upper and lower bounds describing this anomalous diffusion are obtained.

Exponential energy growth in adiabatically changing Hamiltonian systems.

We show that the mixed phase space dynamics of a typical smooth Hamiltonian system universally leads to a sustained exponential growth of energy at a slow periodic variation of parameters. We build a model for this process in terms of geometric Brownian motion with a positive drift, and relate it to the steady entropy increase after each period of the parameters variation.

Solvability of Nonautonomous Fractional Integrodifferential Equations with Infinite Delay

The critical hyperbola for a Hamiltonian elliptic system with weights

In this paper we look for existence results for nontrivial solutions to the system, ⎧ ⎪⎪⎨ ⎪⎪⎩ − u = v p |x |α in , − v = u q |x |β in , with Dirichlet boundary conditions, u = v = 0 on ∂ and α, β < N . We find the existence of a critical hyperbola in the (p, q) plane (depending on α, β and N ) below which there exists nontrivial solutions. For the proof we use a variational argument (a linking ...

Lagrangian and Hamiltonian Mechanics with Fractional Derivatives

In this paper we discuss the fractional extention of classical Lagrangian and Hamiltonian mechanics. We give a view of the mathematical tools associated with fractional calculus as well as a description of some applications.