Hamiltonian Systems: Stability and Instability Theory
Patrick Bernard (CEREMADE)
TL;DR
This paper provides a concise overview of key theories in Hamiltonian systems, including Nekhoroshev, KAM, and Arnold's diffusion, highlighting their roles in understanding stability and instability.
Contribution
It offers a brief survey summarizing fundamental results and concepts in the stability and instability of Hamiltonian systems.
Findings
Nekhoroshev theory explains long-term stability.
KAM theory describes persistence of quasi-periodic motions.
Arnold's diffusion illustrates mechanisms of instability.
Abstract
This is a short survey on Nekhoroshev theory, KAM theory, and Arnold's diffusion.
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