tMapHenon< NumType > Class Template Reference

The Henon map. More...

#include <maphenon.h>

Public Types
typedef NumType	NumberType
	The type of numbers in the Henon map. More...

Public Member Functions
	tMapHenon (const NumType &aNumerator=14, const NumType &aDenominator=10, const NumType &bNumerator=3, const NumType &bDenominator=10)
	The constructor of a Henon map object. More...
void	initialPoint (NumType *x, int iterCount) const
	Returns an initial point for constructing a cover of the attractor. More...
template<class InputType , class ResultType >
void	image (const InputType *xMin, const InputType *xMax, ResultType *yMin, ResultType *yMax) const
	Returns a rigorous bound of the image of the given rectangle by the Henon map. More...

Static Public Member Functions
static int	dim ()
	Returns the dimension of the phase space. More...

Private Attributes
const NumType	aMin
	A lower bound for the parameter 'a' in the Henon map. More...
const NumType	aMax
	An upper bound for the parameter 'a' in the Henon map. More...
const NumType	bMin
	A lower bound for the parameter 'b' in the Henon map. More...
const NumType	bMax
	An upper bound for the parameter 'b' in the Henon map. More...

Detailed Description

template<class NumType>
class tMapHenon< NumType >

The Henon map.

This class defines the Henon map: (x,y) -> (1 + y - ax^2, bx), where a = 1.4 and b = 0.3.

Definition at line 54 of file maphenon.h.

Member Typedef Documentation

NumberType

template<class NumType >

typedef NumType tMapHenon< NumType >::NumberType

The type of numbers in the Henon map.

Definition at line 58 of file maphenon.h.

Constructor & Destructor Documentation

tMapHenon()

template<class NumType >

tMapHenon< NumType >::tMapHenon ( const NumType &  aNumerator = 14, const NumType &  aDenominator = 10, const NumType &  bNumerator = 3, const NumType &  bDenominator = 10  )

inline

The constructor of a Henon map object.

Definition at line 100 of file maphenon.h.

References tMapHenon< NumType >::aMin, and tMapHenon< NumType >::bMin.

Member Function Documentation

dim()

template<class NumType >

int tMapHenon< NumType >::dim ( )

inlinestatic

Returns the dimension of the phase space.

Definition at line 113 of file maphenon.h.

image()

template<class NumType >

template<class InputType , class ResultType >

void tMapHenon< NumType >::image	(	const InputType *	xMin,
		const InputType *	xMax,
		ResultType *	yMin,
		ResultType *	yMax
	)		const

Returns a rigorous bound of the image of the given rectangle by the Henon map.

Definition at line 135 of file maphenon.h.

References tMapHenon< NumType >::aMax, tMapHenon< NumType >::aMin, tMapHenon< NumType >::bMax, tMapHenon< NumType >::bMin, and openSqr().

Referenced by tMapHenon< NumType >::initialPoint().

initialPoint()

template<class NumType >

void tMapHenon< NumType >::initialPoint ( NumType *  x, int  iterCount  ) const

inline

Returns an initial point for constructing a cover of the attractor.

The vector provided is iterated for the given time by the map, and the result is stored back in the provided vector.

Definition at line 119 of file maphenon.h.

References tMapHenon< NumType >::aMin, tMapHenon< NumType >::bMin, and tMapHenon< NumType >::image().

Member Data Documentation

aMax

template<class NumType >

const NumType tMapHenon< NumType >::aMax

private

An upper bound for the parameter 'a' in the Henon map.

Definition at line 86 of file maphenon.h.

Referenced by tMapHenon< NumType >::image().

aMin

template<class NumType >

const NumType tMapHenon< NumType >::aMin

private

A lower bound for the parameter 'a' in the Henon map.

Definition at line 83 of file maphenon.h.

Referenced by tMapHenon< NumType >::image(), tMapHenon< NumType >::initialPoint(), and tMapHenon< NumType >::tMapHenon().

bMax

template<class NumType >

const NumType tMapHenon< NumType >::bMax

private

An upper bound for the parameter 'b' in the Henon map.

Definition at line 92 of file maphenon.h.

Referenced by tMapHenon< NumType >::image().

bMin

template<class NumType >

const NumType tMapHenon< NumType >::bMin

private

A lower bound for the parameter 'b' in the Henon map.

Definition at line 89 of file maphenon.h.

Referenced by tMapHenon< NumType >::image(), tMapHenon< NumType >::initialPoint(), and tMapHenon< NumType >::tMapHenon().

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The documentation for this class was generated from the following file:

• maphenon.h