Torus Deformation Theory#

pyna.toroidal.torus_deformation contains the analytic torus-deformation tools used to study how invariant tori and resonant structures respond to controlled perturbations.

Conceptual Role#

In the geometry hierarchy:

  • an invariant torus is an InvariantTorus;

  • a resonant elliptic cycle is the core of a Tube;

  • a hyperbolic cycle bounds a tube and generates stable/unstable manifolds;

  • cutting tubes with a Poincare section produces IslandChain objects.

Torus-deformation calculations therefore feed directly into topology control: they predict which spectral perturbations move, split, heal or suppress resonant structures.

Public API#