How to compute the Melnikov vector?

ABSTRACT

It is shown that transverse homoclinic intersections such as the ones described by the Melnikov theory can be computed by a local analysis of the complex-time singularities of the solutions. This provides a new algorithmic procedure to compute homoclinic intersections in n-dimensions once the homoclinic manifold is known. It also gives new insights on the singularity structure of integrable and nonintegrable systems.

REFERENCES

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.2 Nonnumerical Algorithms and Problems
          Subjects: Computations on discrete structures

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

General Terms:
Algorithms, Theory