omnibias.dynamics
Computer-assisted dynamics on the validated tower. Rigorous (interval /
Taylor-model) tools for nonlinear dynamical systems, built on the QR-Lohner
validated flow and the radii-polynomial existence machinery in
omnibias.core.verified.
import omnibias.dynamics as od
An enclosure provably contains the true object, and an existence claim is a proof, never a heuristic.
Variational / monodromy flow
Propagate a state and its fundamental (variational) matrix rigorously — the basis for Floquet / stability analysis.
| Symbol | Role |
|---|---|
variational_flow, variational_step | rigorous state + variational-matrix flow |
VariationalState | the enclosed state container |
step_transition_matrix | per-step transition matrix enclosure |
monodromy_matrix, monodromy_trace, monodromy_determinant | monodromy quantities |
spectral_radius_bound | enclosure of the spectral radius |
Poincaré sections
PoincareSection · PoincareCrossing · poincare_map — a rigorous return map
across a hyperplane.
Certified Lyapunov bounds
certified_lyapunov_exponent → LyapunovBounds — two-sided enclosures of the
leading Lyapunov exponent from the validated variational flow.
Periodic-orbit proofs
prove_periodic_orbit → PeriodicOrbitCertificate — a radii-polynomial proof
that a true periodic orbit lives in an explicit ball around a numerical guess.
Example systems
harmonic_oscillator · linear_system · radial_logistic ·
hopf_normal_form — ready-made vector fields for trying the tools.
Example
from omnibias.dynamics import prove_periodic_orbit, hopf_normal_form
cert = prove_periodic_orbit(hopf_normal_form(mu=0.5), guess=initial_loop)
print(cert) # proven / not proven, with the enclosing ball radius