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$$
\begin{aligned}
& q \to p \\
& p \to -q + w p + p^2
\end{aligned}
$$
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
About
Computation of bifurcation fractals for 2D symplectic mappings