Hamiltonian and Symplectic Dynamics
KAM theory, integrable systems, and Arnold diffusion.
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 · 1989Mathematical Methods of Classical Mechanicsarnold-1989
- textbook · supporting · 1978Foundations of Mechanicsabraham-1978, marsden-1978
In context
Where this topic sits in the prerequisite graph. Click any node to jump.
Review this topic
This page was drafted by an agent and is waiting on expert review. Spotted a wrong prerequisite, a missing concept, a misattributed source, or a factual slip? Tell us — your review opens a tracked issue maintainers act on.