We derive a family of singular iterated maps--closely related to Poincare maps--that describe chaotic interactions between colliding solitary waves. The chaotic behavior of such solitary-wave collisions depends on the transfer of energy to a secondary mode of oscillation, often an internal mode of the pulse. This map allows us to go beyond previous analyses and to understand the interactions in...

The nature of elastic deformation is examined in the light of the potential theory. The concepts and mathematical treatment of elasticity and the choice of equilibrium conditions are adopted from the mechanics of discrete bodies, e. g., celestial mechanics; they are not applicable to a change of state. By nature, elastic deformation is energetically a Poisson problem since the buildup of an ela...

— Most physical systems are modelled by an ordinary or a partial differential equation, like the n-body problem in celestial mechanics. In some cases, for example when studying the long term behaviour of the solar system or for complex systems, there exist elements which can influence the dynamics of the system which are not well modelled or even known. One way to take these problems into accou...

This paper deals with the e ective computation of normal forms, centre manifolds and rst integrals in Hamiltonian mechanics. These kind of calculations are very useful since they allow, for instance, to give explicit estimates on the di usion time or to compute invariant tori. The approach presented here is based on using algebraic manipulation for the formal series but taking numerical coe cie...

We extend the Newtonian n-body problem of celestial mechanics to spaces of curvature κ = constant and provide a unified framework for studying the motion. In the 2-dimensional case, we prove the existence of several classes of relative equilibria, including the Lagrangian and Eulerian solutions for any κ 6= 0 and the hyperbolic rotations for κ < 0. These results lead to a new way of understandi...

Knowledge about stable and unstable manifolds of hyperbolic fixed points of certain maps is desirable in many fields of research, both in pure mathematics as well as in applications, ranging from forced oscillations to celestial mechanics and space mission design. We present a technique to find highly accurate polynomial approximations of local invariant manifolds for sufficiently smooth planar...