28 May, 2026

Notes

2026-10-30

To do!

• original paper by Henon and Heiles @Henon1964

yesterdays todo’s:*

• investigation of ‘How to implement?’ and ‘How to visiualize?’
• simple implementation of various and visualization

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

@Henon1964 - on isolating and non isolating integrals A CLASSIFICATION OF THE INTEGRALS OF MOTION by George Contopoulos

Citation @Henon1964: On the argument of 2 or 3 non isolating integrals.

Citation @Henon1964: 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 @Henon1964: Statements and potential open questions.

• “but the dimensions are so small that finding them is difficult” – is how the term dimensions gets used again