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Class ChaosDemos.periodicOrbits 

java.lang.Object
   |
   +----ChaosDemos.periodicOrbits
public class periodicOrbits
extends Object
Finds and characterizes periodic orbits

Version:
21 April 1999
Author:
Michael Cross

Variable Index

o addPoint
true if new fixed point curve should be added to graph
o eig1
Eigenvalues
o eig2
o ev1
Eigenvectors and adjoints
o ev2
o foundFirst
true of found first point near periodic orbit
o foundFixedPoint
true if found ith fixed point
o foundOrbit
true if point near periodic orbit
o fp
Current best estimate of periodic points
o fv1
o fv2
o nIterates
Numberof iterates[period] stored for each periodic point
o nOrbits
Number of orbits
o partOfOrbit
true if point part of working orbit
o period
Period of orbit

Constructor Index

o periodicOrbits(int)

Method Index

o returnOrbit()
Returns array containing periodic orbit in format for plotting x1,y1,x2,y2.....
o setFitNumber(int)
Sets the number of points accumulated before a fit is done
o setTolerance(double, double)
Sets tolerances eps1, eps2
o testPoint(double[])
Tests to see if point is part of periodic orbit and stores point for future test.
o updateFit(double[][])
Updates current best estimate of periodic orbit

Variables

o period 
 int period
Period of orbit

o nOrbits 
 public int nOrbits
Number of orbits

o nIterates 
 int nIterates[]
Numberof iterates[period] stored for each periodic point

o fp 
 public double fp[][]
Current best estimate of periodic points

o eig1 
 public double eig1[]
Eigenvalues

o eig2 
 public double eig2[]
o ev1 
 public double ev1[][]
Eigenvectors and adjoints

o ev2 
 public double ev2[][]
o fv1 
 public double fv1[][]
o fv2 
 public double fv2[][]
o foundFixedPoint 
 public boolean foundFixedPoint[]
true if found ith fixed point

o addPoint 
 public boolean addPoint[]
true if new fixed point curve should be added to graph

o foundFirst 
 public boolean foundFirst
true of found first point near periodic orbit

o foundOrbit 
 public boolean foundOrbit
true if point near periodic orbit

o partOfOrbit 
 public boolean partOfOrbit
true if point part of working orbit

Constructors

o periodicOrbits 
 public periodicOrbits(int inPeriod)

Methods

o setTolerance 
 public void setTolerance(double eps1,
                          double eps2)
Sets tolerances eps1, eps2

Parameters:
eps2 - For a period p orbit the pth iterate must be within a ditance eps1 and intermediate points must be outside a distance eps2
o setFitNumber 
 public void setFitNumber(int N)
Sets the number of points accumulated before a fit is done

Parameters:
N: - the number of points
o testPoint 
 public int testPoint(double point[])
Tests to see if point is part of periodic orbit and stores point for future test.

Parameters:
point - contains x and y coordinates as first two entries
o returnOrbit 
 public double[] returnOrbit()
Returns array containing periodic orbit in format for plotting x1,y1,x2,y2.....

o updateFit 
 public void updateFit(double inFp[][])
Updates current best estimate of periodic orbit

Parameters:
inFp - array containing orbit in format x1,y1,x2,y2.... 
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