Henon's trick for calculating Poincare section?

[yuxi-liu-wired]

I saw an interesting trick for PSOS in the very short (3 pages) note

Henon, M., ‘On the Numerical Computation of Poincaré Maps’, Physica D: Nonlinear Phenomena, 5.2–3 (1982), 412–14 https://doi.org/10/fm6qc9

The current code for PSOS, and it uses a root-finding algorithm to find the precise time needed to step the integration. In Henon's paper, he suggests transforming the ODE to solve for the precise time as a dependent variable, so the accuracy of solving for time would be the same accuracy as one step of the ODE solver.

I wonder if it's worth implementing in terms of increasing accuracy?

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[Datseris]

In general sounds good, my concern would be mostly about actually implementing this, and the performance defecit; I think the version we have right now is quite performant.

[Datseris]

But of course, this doesn't have to remove the existing poincaresos, just add another function, like henonsos :D