The Finite Resolution Dynamics Software
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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... | |
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.
typedef NumType tMapHenon< NumType >::NumberType |
The type of numbers in the Henon map.
Definition at line 58 of file maphenon.h.
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inline |
The constructor of a Henon map object.
Definition at line 100 of file maphenon.h.
References tMapHenon< NumType >::aMin, and tMapHenon< NumType >::bMin.
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inlinestatic |
Returns the dimension of the phase space.
Definition at line 113 of file maphenon.h.
void tMapHenon< NumType >::image | ( | const InputType * | xMin, |
const InputType * | xMax, | ||
ResultType * | yMin, | ||
ResultType * | yMax | ||
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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().
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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().
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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().
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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().
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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().
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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().