Class StandardMap

java.lang.Object
org.episteme.core.mathematics.analysis.chaos.StandardMap
All Implemented Interfaces:
Function<Point2D,Point2D>, DiscreteMap<Point2D>, Function<Point2D,Point2D>, Relation<Point2D,Point2D>
public class StandardMap extends Object implements DiscreteMap<Point2D>
The Standard Map (Chirikov-Taylor map): p_{n+1} = (p_n + K * sin(theta_n)) mod 2Ï€ theta_{n+1} = (theta_n + p_{n+1}) mod 2Ï€

An area-preserving chaotic map from a square with side 2Ï€ onto itself. Used to model the motion of a kicked rotator.

Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Constructor Details

    • StandardMap

      public StandardMap(double K)
      Creates a Standard Map with parameter K.
      Parameters:
      K - the stochasticity parameter

  • Method Details

    • evaluate

      public Point2D evaluate(Point2D state)
      Description copied from interface: Function
      Evaluates this function at the given point.
      Specified by:
      evaluate in interface Function<Point2D,Point2D>
      Parameters:
      state - 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