Hamiltonian and Symplectic Dynamics

KAM theory, integrable systems, and Arnold diffusion.


field tier

Hamiltonian and Symplectic Dynamics. KAM theory, integrable systems, and Arnold diffusion.

Foundations and canonical references

The standard treatments of hamiltonian and symplectic dynamics approach the subject from complementary angles. Arnold, Mathematical Methods of Classical Mechanics (1989) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Abraham, Foundations of Mechanics (1978) offers an alternative presentation that complements the primary references and is useful for triangulating definitions and proof techniques.

Open methodological questions for hamiltonian and symplectic dynamics include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.

Prerequisites

Sources

  • textbook · primary · 1989
    Mathematical Methods of Classical Mechanics
    arnold-1989
  • textbook · supporting · 1978
    Foundations of Mechanics
    abraham-1978, marsden-1978

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