Appendix

The following sections are included:

• Appendix A: Kolmogorov's 1954 paper

• Appendix B: Overview of Low-dimensional Small Divisor Problems

  • The linearization problem

    • From Schröoder's functional equation to the Siegel center problem

    • Refinements and optimal conditions for the Siegel problem

  • Mappings of the circle

• Appendix C: East Meets West — Russians, Europeans, Americans

  • Cultural stereotypes in mathematics

  • Cultural and stylistic tensions

  • Cultural cross-currents in KAM theory

• Appendix D: Guide to Further Reading

  • General references on KAM

    • Original KAM articles, and priority

    • Accessible proofs of KAM theorems

    • Books on KAM theory (what books?)

    • Review articles, monographs, & book chapters on KAM

    • Expository, historical, & other sources on KAM

  • Mathematical background

    • Dynamical systems and ODEs

    • Classical mechanics and Hamiltonian dynamics

    • Ergodic theory

  • Chaos theory

    • The popular side of chaos

    • A chaos debate

    • The aftermath of popular chaos theory

  • History

    • The special nature of history of math & physics

    • Early history of mathematics and astronomy

    • Between Newton and Poincaré

    • Weierstrass and Poincaré's time

    • The Painlevé conjecture & the n body problem

    • The Soviet & Russian schools of dynamical systems

    • History of dynamical systems in general

  • Biography

    • General biographical sources

    • The principals

  • Applications of KAM (and Nekhoroshev) theory

    • Applications to celestial mechanics; stability

    • Applications to statistical mechanics, ergodic theory

    • Other applications

  • Mathematical topics related to classical KAM theory

    • Low-dimensional small divisor problems

    • Aubry-Mather & weak KAM theory, KAM for PDE

    • Nekhoroshev theory

    • Arnold diffusion

  • Culture, philosophy, Bourbaki, etc.

• Appendix E: Selected Quotations

• Appendix F: Glossary