Expectations, Price Fluctuations and Lorenz Attractor
نویسندگان
چکیده
منابع مشابه
The Lorenz Attractor Exists
We prove that the Lorenz equations support a strange attractor, as conjectured by Ed-ward Lorenz in 1963. We also prove that the attractor is robust, i.e., it persists under small perturbations of the coeecients in the underlying diierential equations. The proof is based on a combination of normal form theory and rigorous numerical computations.
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The Lorenz attractor was once thought to be the mathematically simplest autonomous dissipative chaotic flow, but it is now known that it is only one member of a very large family of such systems, many of which are even simpler. Even the system originally proposed by Lorenz is not in its simplest possible form. This paper will describe a number of simplifications that can be made to the Lorenz s...
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Ideally an embedding of an N -dimensional dynamical system is N -dimensional. Ideally, an embedding of a dynamical system with symmetry is symmetric. Ideally, the symmetry of the embedding is the same as the symmetry of the original system. This ideal often cannot be achieved. Differential embeddings of the Lorenz system, which possesses a twofold rotation symmetry, are not ideal. While the dif...
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ژورنال
عنوان ژورنال: SSRN Electronic Journal
سال: 2018
ISSN: 1556-5068
DOI: 10.2139/ssrn.3253090