Class HenonMap

java.lang.Object
org.episteme.core.mathematics.analysis.chaos.HenonMap
All Implemented Interfaces:
Function<Point2D,Point2D>, DiscreteMap<Point2D>, Function<Point2D,Point2D>, Relation<Point2D,Point2D>
public class HenonMap extends Object implements DiscreteMap<Point2D>
The Hénon Map: x_{n+1} = 1 - a * x_n^2 + y_n y_{n+1} = b * x_n

A discrete-time dynamical system that exhibits chaotic behavior. Classic values: a = 1.4, b = 0.3.

References

  • Michel Hénon, "A two-dimensional mapping with a strange attractor", Communications in Mathematical Physics, Vol. 50, No. 1, 1976, pp. 69-77
Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Constructor Details

    • HenonMap

      public HenonMap()
      Creates a Hénon Map with default chaotic parameters (a=1.4, b=0.3).

    • HenonMap

      public HenonMap(double a, double b)
      Creates a Hénon Map with specified parameters (double precision).

      For arbitrary precision, use HenonMap(Real, Real).

      Parameters:
      a - parameter a
      b - parameter b

    • HenonMap

      public HenonMap(Real a, Real b)
      Creates a Hénon Map with specified parameters (arbitrary precision).
      Parameters:
      a - parameter a
      b - parameter b

  • 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

    • getA

      public Real getA()
      Gets parameter a.
      Returns:
      parameter a

    • getB

      public Real getB()
      Gets parameter b.
      Returns:
      parameter b

    • 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