Class ArnoldCatMap

java.lang.Object

org.episteme.core.mathematics.analysis.chaos.ArnoldCatMap

All Implemented Interfaces:

Function<Point2D,Point2D>, DiscreteMap<Point2D>, Function<Point2D,Point2D>, Relation<Point2D,Point2D>

public class ArnoldCatMap
extends Object
implements DiscreteMap<Point2D>

Arnold's Cat Map: x_{n+1} = (2x_n + y_n) mod 1 y_{n+1} = (x_n + y_n) mod 1

A chaotic map from the torus into itself. It is an example of an Anosov diffeomorphism.

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
ArnoldCatMap()

Method Summary

Modifier and Type	Method	Description
Point2D	evaluate(Point2D p)	Evaluates this function at the given point.
String	getCodomain()	Returns the codomain description.
String	getDomain()	Returns the domain description.
String	toString()

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface DiscreteMap

getLyapunovExponent, iterate

Methods inherited from interface Function

compose

Methods inherited from interface Function

andThen, apply, compose, contains, evaluate, getBackend, isContinuous, isDifferentiable, setBackend

Constructor Details

ArnoldCatMap

public ArnoldCatMap()

Method Details

evaluate

public Point2D evaluate(Point2D p)

Description copied from interface: Function

Evaluates this function at the given point.

Specified by:

evaluate in interface Function<Point2D,Point2D>

Parameters:

p - the input point

Returns:

the value of the function at x

getDomain

public String getDomain()

Description copied from interface: Relation

Returns the domain description.

Specified by:

getDomain in interface Relation<Point2D,Point2D>

Returns:

domain name (e.g., "ℝ", "ℕ", "ℂ")

getCodomain

public String getCodomain()

Description copied from interface: Relation

Returns the codomain description.

Specified by:

getCodomain in interface Relation<Point2D,Point2D>

Returns:

codomain name

toString

public String toString()

Overrides:

toString in class Object