IMFFatTrajectory
[IMFComputeInvariantManifold]

Collaboration diagram for IMFFatTrajectory:

Classes
class	IMFFatTrajectory
	A fat trajectory is a trajectory in a flow with a local expansion attached that also evolves. More...
Functions
void	IMFExtendAtlasAlongFatTraj (MFAtlas I, IMFFlow F, MFNVector u0, MFKVector p0, double dt, double ti, double tf, double epsilon, MFNRegion Omega, int maxSteps, int maxCharts, double Rmax, int nSkip, MFErrorHandler e)
	Integrates a fat trajectory and adds the points to an atlas.
MFChart	IMFStepAlongFatTraj (MFAtlas I, IMFFlow F, MFNVector u0, MFKVector p0, double R0, double dt, double epsilon, MFNRegion Omega, double Rmax, MFErrorHandler e)
	Integrates one step along a fat trajectory.

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Function Documentation

void IMFExtendAtlasAlongFatTraj (  MFAtlas  I, IMFFlow  F, MFNVector  u0, MFKVector  p0, double  dt, double  ti, double  tf, double  epsilon, MFNRegion  Omega, int  maxSteps, int  maxCharts, double  Rmax, int  nSkip, MFErrorHandler  e )

Integrates a fat trajectory and adds the points to an atlas. Parameters: I  The atlas to which new charts will be added. F  The flow. u0  The initial point on the fat trajectory. p0  The flow parameters. dt  The initial time step. ti  The initial time. tf  The upper limit on time. epsilon  The maximum allowed size of the second order terms within a ball. Determines the stepsize. Omega  A region to limit the computation. maxSteps  The maximum number of steps to take along the fat trajectory. maxCharts  The maximum number of charts allowed in the atlas. Rmax  The largest radius of a ball. nSkip  The number of steps to make without adding points to the atlas. e  A place to return errors.

MFChart IMFStepAlongFatTraj (  MFAtlas  I, IMFFlow  F, MFNVector  u0, MFKVector  p0, double  R0, double  dt, double  epsilon, MFNRegion  Omega, double  Rmax, MFErrorHandler  e )

Integrates one step along a fat trajectory. Parameters: I  The atlas to which new charts will be added. F  The flow. u0  The initial point on the fat trajectory. p0  The flow parameters. R0  The distance requested between initial and final points of the step. dt  The initial time step. epsilon  The maximum allowed size of the second order terms within a ball. Determines the stepsize. Omega  A region to limit the computation. Rmax  The largest radius of a ball. e  A place to return errors. Returns: A new chart along the fat trajectory.

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