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It is known that as parameters vary in Hamiltonian system, KAM tori can break [1,2].

How to construct numerically the breaking tori?

The most relevant paper that I could find is [3,4].

But it uses chaos indicator for its bifurcation plots. I.e., it does not concern itself with actual construction of tori.

[1] MacKay, R. S., Renormalisation in area-preserving maps, Advanced Series in Nonlinear Dynamics. 6. Singapore: World Scientific. xix, 304 p. (1993). ZBL0791.58002.

[2] Delshams, Amadeu; de la Llave, Rafael; Seara, Tere M., A geometric mechanism for diffusion in Hamiltonian systems overcoming in the large gap problem: Heuristics and rigorous verification on a model, Mem. Am. Math. Soc. 844, 141 p. (2006). ZBL1090.37044.

[3] @article{barrio2020distribution, title={Distribution of stable islands within chaotic areas in the non-hyperbolic and hyperbolic regimes in the H{'e}non--Heiles system}, author={Barrio, Roberto and Wilczak, Daniel}, journal={Nonlinear Dynamics}, volume={102}, number={1}, pages={403--416}, year={2020}, publisher={Springer} }

[4] @article{aguirre2001wada, title={Wada basins and chaotic invariant sets in the H{'e}non-Heiles system}, author={Aguirre, Jacobo and Vallejo, Juan C and Sanju{'a}n, Miguel AF}, journal={Physical Review E}, volume={64}, number={6}, pages={066208}, year={2001}, publisher={APS} }

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  • $\begingroup$ I tried to improve the formatting of your citations by using the automatic citation tool, but references [3] and [4] were not found by the system. $\endgroup$
    – Sam Hopkins
    Commented Aug 14, 2023 at 15:40
  • $\begingroup$ Cantori or KAM tori?? $\endgroup$
    – YCor
    Commented Aug 14, 2023 at 20:33
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    $\begingroup$ @YCor Cantori , as defined e.g. in Mackay "Cantori for symplectic maps near the anti-integrable limit" $\endgroup$
    – 0x11111
    Commented Aug 18, 2023 at 12:18

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