This chapter discusses Hamiltonian dynamics, a type of dynamical system that combines linear systems and manifolds and has applications in medicine, physics, and computer graphics.Expand

Symplectic maps are the discrete-time analog of Hamiltonian motion. They arise in many applications including accelerator, chemical, condensed-matter, plasma, and fluid physics. Twist maps correspond… Expand

Abstract We develop a theory of transport in Hamiltonian systems in the context of iteration of area-preserving maps. Invariant closed curves present complete barriers to transport, but in regions… Expand

Abstract Transport times for a chaotic system are highly sensitive to initial conditions and parameter values. In a previous paper, we presented a technique to find rough orbits (epsilon chains) that… Expand

The survival probability distribution is shown to decay asymptotically as a power law and the decay exponent agrees reasonably well with the computations of Karney and of Chirikov and Shepelyanski.Expand

Here Dfij = ∂fi/∂zj is the Jacobian matrix of f , J is the Poisson matrix, and I is the n × n identity matrix. Equivalently, Stokes’ theorem can be used to show that the loop action, A[γ] = ∮ γ pdq,… Expand

Abstract A 2 N -dimensional symplectic mapping which satisfies the twist condition is obtained from a Lagrangian generating function F ( q , q ′) . The q 's are assumed to be angle variables.… Expand

We develop a general theory of implicit generating forms for volume-preserving diffeomorphisms on a manifold. Our results generalize the classical formulas for generating functions of symplectic… Expand

This work identifies the mechanism that generates extremely complicated orbit structures in population models, including islands-around-islands, ad infinitum, with the smaller islands containing stable periodic points of higher period.Expand