IMFComputeInvariantManifold
[IMF]

Collaboration diagram for IMFComputeInvariantManifold:

Modules
	IMFFatTrajectory
Classes
class	IMFComputeInvariantManifold
	A group of routines to compute invariant manifolds. More...
Functions
MFAtlas	IMFComputeStableInvariantManifold (IMFFlow F, char *name, MFNVector u0, MFKVector p0, MFNRegion Omega, double eps, double dt, double tmax, int maxInterp, int maxCharts, double R0, MFErrorHandler e)
	Computes an atlas of charts that cover the stable manifold of a hyerbolic fixed point.
MFAtlas	IMFComputeUnstableInvariantManifold (IMFFlow F, char *name, MFNVector u0, MFKVector p0, MFNRegion Omega, double eps, double dt, double tmax, int maxInterp, int maxCharts, double R0, MFErrorHandler e)
	Computes an atlas of charts that cover the unstable manifold of a hyerbolic fixed point.
MFAtlas	IMFComputeInvariantManifold (IMFFlow F, MFKVector p0, char *name, MFAtlas c, MFNRegion Omega, double eps, double dt, double tmax, int maxInterp, int maxCharts, double Rmax, MFErrorHandler e)
	Computes an atlas of charts that cover the image of a manifold under a flow. A streamsurface.

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Function Documentation

MFAtlas IMFComputeInvariantManifold (  IMFFlow  F, MFKVector  p0, char *  name, MFAtlas  c, MFNRegion  Omega, double  eps, double  dt, double  tmax, int  maxInterp, int  maxCharts, double  Rmax, MFErrorHandler  e )

Computes an atlas of charts that cover the image of a manifold under a flow. A streamsurface. Parameters: F  The flow. name  A name to used for paging files and so forth. p0  The parameters of the flow for the fixed point. c  The manifold of initial conditions. Omega  A region to bound the computation. eps  The tolerance on the size of the quadratic terms over a balls. Controls the stepsize. dt  The initial timestep to use along a fat trajectory. tmax  The upper limit on trajectory length. maxInterp  The upper limit on the number of interpolation performed. maxCharts  The upper limit on the number of charts in the atlas. Rmax  An upper limit to impose on the radius of the balls along the fat trajectories. e  A place to return errors. Returns: A new Atlas

MFAtlas IMFComputeStableInvariantManifold (  IMFFlow  F, char *  name, MFNVector  u0, MFKVector  p0, MFNRegion  Omega, double  eps, double  dt, double  tmax, int  maxInterp, int  maxCharts, double  R0, MFErrorHandler  e )

Computes an atlas of charts that cover the stable manifold of a hyerbolic fixed point. Parameters: F  The flow. name  A name to used for paging files and so forth. u0  The fixed point. p0  The parameters of the flow for the fixed point. Omega  A region to bound the computation. eps  The tolerance on the size of the quadratic terms over a balls. Controls the stepsize. dt  The initial timestep to use along a fat trajectory. tmax  The upper limit on trajectory length. maxInterp  The upper limit on the number of interpolation performed. maxCharts  The upper limit on the number of charts in the atlas. R0  The radius for the initial ball about the fixedpoint that serves as initial surface for the manifold. e  A place to return errors. Returns: A new Atlas

MFAtlas IMFComputeUnstableInvariantManifold (  IMFFlow  F, char *  name, MFNVector  u0, MFKVector  p0, MFNRegion  Omega, double  eps, double  dt, double  tmax, int  maxInterp, int  maxCharts, double  R0, MFErrorHandler  e )

Computes an atlas of charts that cover the unstable manifold of a hyerbolic fixed point. Parameters: F  The flow. name  A name to used for paging files and so forth. u0  The fixed point. p0  The parameters of the flow for the fixed point. Omega  A region to bound the computation. eps  The tolerance on the size of the quadratic terms over a balls. Controls the stepsize. dt  The initial timestep to use along a fat trajectory. tmax  The upper limit on trajectory length. maxInterp  The upper limit on the number of interpolation performed. maxCharts  The upper limit on the number of charts in the atlas. R0  The radius for the initial ball about the fixedpoint that serves as initial surface for the manifold. e  A place to return errors. Returns: A new Atlas

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