celeries.mmr.MMR.fp_normalform

MMR.fp_normalform(v_fp, delta, order, resonances=None, clean_epsilon=None)

Compute the Birkhoff normal form (birkhoff.NormalForm) around a fixed point.

Parameters:

v_fp(4*npla-4,) ndarray

Coordinates of the fixed point.

deltafloat

Value of delta (normalized by Gamma).

orderint

Order of the expansion of the normal form (see birkhoff.NormalForm).

resonances(nr, ndof) ndarray or None

Resonances to keep in the normal form (as well as any combination).

clean_epsilonfloat or None

Threshold to delete small coefficients from the Hamiltonian (if provided), before computing the normal form.

Returns:

nfNormalForm

Normal form of the Hamiltonian around the fixed point.

eig_val(4*npla-4,) ndarray

Eigenvalues of the quadratic part.

eig_vec(4*npla-4, 4*npla-4) ndarray

Matrix Q of the symplectic change of variables applied before computing the normal form.