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Answer by E. Chan-López for Poincaré section of the particle motion near the...
To detect more islands, it is better to use the interactive method. Here, I provide an example with the result for the case in which the energy is equal to 40.PoincareSections[{x0_, px0_, y0_, py0_},...
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Answer by Alex Trounev for Poincaré section of the particle motion near the...
As mentioned by I.M. the Hamiltonian could be derive with using Legendre transformation - see for example here. Therefore we havek = 1/2;w = 10;c = 1;lagrangian = -Sqrt[2 k x[t] - x'[t]^2/(2 k x[t]) -...
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Answer by I.M. for Poincaré section of the particle motion near the black...
There are several problems with your code:Hamiltonian construction is not correct (you need to solve for velocities in terms of momenta, not just substitute $x' \to p_x$ and $y' \to p_y$)In the linked...
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Poincaré section of the particle motion near the black hole horizon
I am trying to recreate the Poincaré sections given in Figure 2 of this paper.For this purpose, I use the following two methods:Method1: Using ResourceFunction["ClickPoincarePlot2D"] f = 2 k...
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Answer by codebpr for Poincaré section of the particle motion near the black...
The resource function ["ClickPoincarePlot2D"] is also working now, thanks to the new update.I have also used the ScalarPureFunction by @E. Chan-López presented here to simplify my Hamiltonian into a...
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