Isochronicity and linearizability of two-dimensional polynomial Hamiltonian systems are revisited new results presented. We give a computational procedure to obtain the necessary sufficient conditions for linearization system. Using computer algebra we provide with homogeneous non-linearities degrees 5, 6 7. also present some nonhomogeneous nonlinearities two, three five.

In this work, we devise a stochastic version of contact Hamiltonian systems and show that the phase flows these preserve structures. Moreover, provide sufficient condition under which are completely integrable. This establishes an appropriate framework for investigating systems.

We determine the Hamiltonian vector field on an odd dimensional manifold endowed with almost cosymplectic structure. This is a generalization of corresponding manifolds transitive contact structures, which extends systems. Applications are presented to equations motion particular five-dimensional manifold, extended Siegel-Jacobi upper-half plane $\tilde{\mathcal{X}}^J_1$. The $\tilde{\mathcal{X...

An overview of Hamiltonian systems with noncanonical Poisson structures is given. Examples of bi-Hamiltonian ode's, pde's and lattice equations are presented. Numerical integrators using generating functions, Hamiltonian splitting, symplectic Runge-Kutta methods are discussed for Lie-Poisson systems and Hamiltonian systems with a general Poisson structure. Nambu-Poisson systems and the discrete...

It is shown how port-based modeling of lumped-parameter complex physical systems (multi-body systems, electrical circuits, electromechanical systems, ..) naturally leads to a geometrically defined class of systems, called port-Hamiltonian systems. These are Hamiltonian systems defined with respect to a power-conserving geometric structure capturing the basic interconnection laws, and a Hamilton...

We show that the nontwist phenomena previously observed in Hamiltonian systems exist also in time-reversible non-Hamiltonian systems. In particular, we study the two standard collision-reconnection scenarios and we compute the parameter space breakup diagram of the shearless torus. Besides the Hamiltonian routes, the breakup may occur due to the onset of attractors. We study these phenomena in ...

We discuss the Sinai method of proving ergodicity of a discontinuous Hamiltonian system with (non-uniform) hyperbolic behavior.

Hamiltonian systems are a class of dynamical systems which can be characterised by preservation of a symplectic form. This allows to write down the equations of motion in terms of a single function, the Hamiltonian function. They were conceived in the 19th century to study physical systems varying from optics to frictionless mechanics in a unified way. This description turned out to be particul...