28 May, 2026

Published

October 30, 2026

Also available as a slide deck.

To do!

yesterdays todo’s:*

checking in

I feel that I should read about implementing the Hénon & Heiles. I should also read their original paper.

Whilst working on Hénon & Heiles, I realize I need to get an in depth understanding of the Lagrange and Hamiltonian formalism!

Notes from Hénon & Heiles

Hénon and Heiles (1964) - on isolating and non isolating integrals A CLASSIFICATION OF THE INTEGRALS OF MOTION by George Contopoulos

Citation Hénon and Heiles (1964): On the argument of 2 or 3 non isolating integrals.

Citation Hénon and Heiles (1964): On finding the second Integral. Leading to an understanding of what it means to be ergodic.

  • I did not understand much of section 2

  • a second read and note shed some light, here is an interesting paragraph describing what ergodic mean

  • a question they seem to be answering is how to find a proof of the existence of an non isolating integral

  • they speak of two integration schemes:

    • Adams
    • Runge-Kutta

  • Their analysis introduces terms as islands and chain of islands, dimension of islands, dense and need to be understood when I study this model

Citation Hénon and Heiles (1964): Statements and potential open questions.
  • “but the dimensions are so small that finding them is difficult” – is how the term dimensions gets used again

References

Hénon, Michel, and Carl Heiles. 1964. “The Applicability of the Third Integral of Motion: Some Numerical Experiments.” The Astronomical Journal 69 (1): 73–79. https://doi.org/10.1086/109234.