IMFFixedPoint
[IMF]

Collaboration diagram for IMFFixedPoint:

Classes
class	IMFFixedPoint
	A group of utilities for computing stable and unstable manifolds of a hyperbolic fixed point. More...
Functions
void	IMFFindExpansionNearFixedPt (MFNVector U0, MFKVector P0, MFNKMatrix Du, MFNKMatrix Dv, IMFFlow F, IMFExpansion U, IMFExpansion a, MFErrorHandler e)
	Given a fixed point in a flow and a decomposition of the phase space into two invariant linear subspaces, creates an expansion of the invariant manifold corresponding to one of the invariant subspaces.
MFNKMatrix	IMFGetBasisForStableInvariantSubspace (IMFFlow F, MFNVector u, MFKVector p, MFErrorHandler e)
	Given a hyperbolic fixed point in a flow, finds a basis for the stable invariant linear subspace of a hyperbolic fixed point.
MFNKMatrix	IMFGetBasisForUnstableInvariantSubspace (IMFFlow F, MFNVector u, MFKVector p, MFErrorHandler e)
	Given a hyperbolic fixed point in a flow, finds a basis for the unstable invariant linear subspace of a hyperbolic fixed point.
MFNKMatrix	IMFGetBasisForOrthogonalComplement (MFNKMatrix Du, MFErrorHandler e)
	Given a linear subspace, finds an orthonormal basis for its orthogonal complement.

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Function Documentation

void IMFFindExpansionNearFixedPt (  MFNVector  U0, MFKVector  P0, MFNKMatrix  Du, MFNKMatrix  Dv, IMFFlow  F, IMFExpansion  U, IMFExpansion  a, MFErrorHandler  e )

Given a fixed point in a flow and a decomposition of the phase space into two invariant linear subspaces, creates an expansion of the invariant manifold corresponding to one of the invariant subspaces. Parameters: U0  The fixed point. P0  The parameters of the flow of the fixed point. Du  The first invariant linear subspace. Dv  The second, complementary invariant linear subspace. F  The flow. U  A user provided expansion in which the expansion defining the surface is placed. a  A user provided expansion in which the expansion defining the complement of the surface is placed. e  A place to return errors.

MFNKMatrix IMFGetBasisForOrthogonalComplement (  MFNKMatrix  Du, MFErrorHandler  e )

Given a linear subspace, finds an orthonormal basis for its orthogonal complement. Parameters: Du  An orthonormal basis a linear subspace. e  A place to return errors. Returns: The orthogonal complement.

MFNKMatrix IMFGetBasisForStableInvariantSubspace (  IMFFlow  F, MFNVector  u, MFKVector  p, MFErrorHandler  e )

Given a hyperbolic fixed point in a flow, finds a basis for the stable invariant linear subspace of a hyperbolic fixed point. Parameters: F  The flow. u  The fixed point. p  The parameters of the flow for the fixed point. e  A place to return errors. Returns: A new MFNKMatrix containing an orthonormal basis for the stable invariant linear subspace of the hyperbolic fixed point.

MFNKMatrix IMFGetBasisForUnstableInvariantSubspace (  IMFFlow  F, MFNVector  u, MFKVector  p, MFErrorHandler  e )

Given a hyperbolic fixed point in a flow, finds a basis for the unstable invariant linear subspace of a hyperbolic fixed point. Parameters: F  The flow. u  The fixed point. p  The parameters of the flow for the fixed point. e  A place to return errors. Returns: A new MFNKMatrix containing an orthonormal basis for the unstable invariant linear subspace of the hyperbolic fixed point.

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