fractal, 2024

Computation of bifurcation fractals for 2D symplectic mappings

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For a quadratic mapping:

$$ \begin{aligned} & q \to p \\ & p \to -q + w p + p^2 \end{aligned} $$

two symmetry lines, $p=q$ and $p=1/2(w q + q^2)$ cover full 2D plane. Fractals bellow are computed in $(w, q)$ space with $w$ in [-3.00, 2.00] and $q$ in [-1.25, 1.75] using the second symmetry line. Color corresponds to different indicators.

• Phase space coverage by symmetry lines

• REM

• Frequency

• Frequency & mode locking (tongues)

• FMA

• GALI