fast_lyapunov_max#

gala.dynamics.nonlinear.fast_lyapunov_max(w0, hamiltonian, dt, n_steps, d0=1e-05, n_steps_per_pullback=10, noffset_orbits=2, t1=0.0, atol=1e-10, rtol=1e-10, nmax=0, return_orbit=True)[source]#

Compute the maximum Lyapunov exponent using a fast C-implemented method.

This function estimates the maximum Lyapunov exponent by integrating the orbit along with several nearby offset orbits and tracking their separation over time. It uses the DOPRI853 integrator for high accuracy.

Parameters:

w0PhaseSpacePosition or array_like: Initial conditions for the primary orbit.
hamiltonianHamiltonian: The Hamiltonian system to integrate in. Must contain a C-implemented potential and frame.
dtfloat: Integration timestep.
n_stepsint: Number of integration steps to run.
d0float, optional: Initial separation between the primary orbit and offset orbits. Default is 1e-5.
n_steps_per_pullbackint, optional: Number of integration steps between each renormalization of the offset vectors. Default is 10.
noffset_orbitsint, optional: Number of offset orbits to use. Default is 2.
t1float, optional: Initial time. Default is 0.0.
atolfloat, optional: Absolute tolerance for the integrator. Default is 1e-10.
rtolfloat, optional: Relative tolerance for the integrator. Default is 1e-10.
nmaxint, optional: Maximum number of function evaluations. Default is 0 (no limit).
return_orbitbool, optional: Whether to return the integrated orbit along with the Lyapunov exponent. Default is True.

Returns:

LEsQuantity: The Lyapunov exponents calculated from each offset orbit.
orbitOrbit, optional: The integrated primary orbit (returned only if return_orbit=True).

Raises:

TypeError: If the Hamiltonian does not contain C-implemented components.
ValueError: If trying to compute Lyapunov exponents for multiple orbits simultaneously.

Notes

The Lyapunov exponent quantifies the rate of exponential divergence of nearby trajectories in phase space. Positive values indicate chaotic motion, while zero or negative values suggest regular motion.

This implementation is optimized for speed and uses C code with the DOPRI853 adaptive Runge-Kutta integrator.