henon-heiles_lyap.h

/*------------------------------------------------------------------------------------

エノン・ハイレス方程式のリアプノフスペクトラムの計算

calculating the Lyapunov spectrum of the Henon-Heiles equations

dx/dt =  z

dy/dt =  w

dz/dt = -x - 2 * x * y

dw/dt = -y - x^2 + y^2

henon-heiles_lyap.h

------------------------------------------------------------------------------------*/

#include <stdio.h>

#include <stdlib.h>

#include <math.h>

#define ITERATION 10000000

// #define ITERATION 100000

#define SKIP      100000

#define DELTA_T 0.001 /* step size of the fourth-order Runge-Kutta method */

// 初期値

// initial values

#define X0  0.50

#define Y0  0.00

#define Z0  0.00

#define W0  0.03

/* Lyapunov spectrum (log with base-e) 0.045, 0, 0, -0.045 */

// 変数の数

// number of variables

#define DIM 4

/*------------------------------------------------------*/

extern void solve_henon_heiles_eqs_using_RK4( double v[DIM], double u[DIM][DIM] );

extern void henon_heiles_eqs( double v[DIM], double dfu[DIM][DIM], double dvdt[DIM], double df_k[DIM][DIM] );

extern void gram_schmidt_orth( double u[DIM][DIM], double e[DIM][DIM] );

extern double calc_lyap_dim( double lambda[DIM] );

extern double log2( double x );