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THE CORRELATION DIMENSION
A NEW ESTIMATE FOR THE CORRELATION
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appropriate attractor with equally basin of attraction Calculated correlation dimension chaotic attractors chaotic system Chapter components correlation dimension estimation correlation dimension values correlation integral delay coordinates delay embedding delayed versions dimension for ground dimension for weather dimension values conditioned discrete discriminating discussed dissipative dynamical systems embedding dimensions error criterion fractional dimension Gaussian noise added Gaussian noise sequence ground clutter ground returns Hausdorff dimension increments information between delayed information dimension initial condition x[0 Koch curve least squares method linear attractor log[C(r log[r logistic equation Lorenz attractor Lorenz system low dimension Lyapunov exponents method and least mutual information function noninteger order Runge-Kutta numerical parameter values phase space plot radar returns random Reconstruction of Lorenz Rossler system Runge-Kutta numerical integration second test single time sequence strange attractor system with zero theoretically topological dimension trajectory unit variance Gaussian variance Gaussian noise vector weather and ground weather returns weighted least squares zero mean