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Introduces a geometric mechanism for diffusion in a priori unstable nearly integrable dynamical systems. This book states that resonances besides destroying the primary KAM tori, create secondary tori and tori of lower dimension.

The aim of this journal is to publish papers in mathematical physics and related areas that are of the highest quality. Research papers and review articles are selected through the normal refereeing process, overseen by an editorial board. The research subjects are primarily on mathematical physics; but this should not be interpreted as a limitation, as the editors feel that essentially all subjects of mathematics and physics are in principle relevant to mathematical physics.

In this monograph the authors introduce a new method to study bifurcations of KAM tori with fixed Diophantine frequency in parameter-dependent Hamiltonian systems. It is based on Singularity Theory of critical points of a real-valued function which the authors call the potential. The potential is constructed in such a way that: nondegenerate critical points of the potential correspond to twist invariant tori (i.e. with nondegenerate torsion) and degenerate critical points of the potential correspond to non-twist invariant tori. Hence, bifurcating points correspond to non-twist tori.

The articles collected in this volume represent the contributions presented at the IMA workshop on Dynamics of Algorithms which took place in November 1997. The workshop was an integral part of the 1997-98 IMA program on Emerging Applications of Dynamical Systems. The interaction between algorithms and dynamical systems is mutually beneficial since dynamical methods can be used to study algorithms that are applied repeatedly. Convergence, asymptotic rates are indeed dynamical properties. On the other hand, the study of dynamical systems benefits enormously from having efficient algorithms to...

The articles collected in this volume represent the contributions presented at the IMA workshop on "Dynamics of Algorithms" which took place in November 1997. The workshop was an integral part of the 1997 -98 IMA program on "Emerging Applications of Dynamical Systems." The interaction between algorithms and dynamical systems is mutually beneficial since dynamical methods can be used to study algorithms that are applied repeatedly. Convergence, asymptotic rates are indeed dynamical properties. On the other hand, the study of dynamical systems benefits enormously from having efficient...