pyna.topo.manifold_improve

Stable and unstable manifold computation for hyperbolic fixed points.

This module supplements the existing pyna.topo.manifold module with object-oriented StableManifold and UnstableManifold classes that take an X-point and its monodromy matrix (from variational equations), grow the manifold by iterating field-line integration, and can plot the result.

Attributes

CynaStableManifold
CynaUnstableManifold

Exceptions

ManifoldWarning

Warning for suspicious manifold growth behavior.

Classes

StableManifold	Stable manifold of a hyperbolic fixed point.
UnstableManifold	Unstable manifold of a hyperbolic fixed point.
ScipyStableManifold	Stable manifold of a hyperbolic fixed point.
ScipyUnstableManifold	Unstable manifold of a hyperbolic fixed point.

Module Contents

exception pyna.topo.manifold_improve.ManifoldWarning

Bases: UserWarning

Warning for suspicious manifold growth behavior.

class pyna.topo.manifold_improve.StableManifold(x_point, DPm, field_func, phi_span=(0.0, 2 * np.pi))

Bases: _ManifoldBase

Stable manifold of a hyperbolic fixed point.

Uses the cyna backend by default for forward one-turn integration and falls back to SciPy when accelerated integration is unavailable or a backward step is required.

class pyna.topo.manifold_improve.UnstableManifold(x_point, DPm, field_func, phi_span=(0.0, 2 * np.pi))

Bases: _ManifoldBase

Unstable manifold of a hyperbolic fixed point.

Uses the cyna backend by default for forward one-turn integration and falls back to SciPy when accelerated integration is unavailable or a backward step is required.

class pyna.topo.manifold_improve.ScipyStableManifold(x_point, DPm, field_func, phi_span=(0.0, 2 * np.pi))

Bases: _ManifoldBase

Stable manifold of a hyperbolic fixed point.

The stable manifold consists of all trajectories that converge to the X-point as the map is iterated forward. Equivalently, seeds on the stable eigenvector are integrated backward in φ.

Inherits from _ManifoldBase. See its documentation for parameter details.

class pyna.topo.manifold_improve.ScipyUnstableManifold(x_point, DPm, field_func, phi_span=(0.0, 2 * np.pi))

Bases: _ManifoldBase

Unstable manifold of a hyperbolic fixed point.

The unstable manifold consists of all trajectories that diverge from the X-point as the map is iterated forward. Seeds on the unstable eigenvector are integrated forward in φ.

Inherits from _ManifoldBase. See its documentation for parameter details.

pyna.topo.manifold_improve.CynaStableManifold

pyna.topo.manifold_improve.CynaUnstableManifold