Embedding the symbolic dynamics of Lorenz maps
نویسندگان
چکیده
منابع مشابه
Symbolic dynamics analysis of the Lorenz equations
Recent progress of symbolic dynamics of oneand especially two-dimensional maps has enabled us to construct symbolic dynamics for systems of ordinary differential equations (ODEs). Numerical study under the guidance of symbolic dynamics is capable to yield global results on chaotic and periodic regimes in systems of dissipative ODEs which cannot be obtained neither by purely analytical means nor...
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A new computational technique based on the symbolic description utilizing kneading invariants is proposed, and verified for explorations of dynamical and parametric chaos in a few exemplary systems with the Lorenz attractor. The technique allows for uncovering the stunning complexity and universality of bi-parametric structures and detects their organizing centers — codimension-two T-points and...
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The butterfly-like Lorenz attractor is one of the best known images of chaos. The computations in this paper exploit symbolic dynamics and other basic notions of hyperbolicity theory to take apart the Lorenz attractor using periodic orbits. We compute all 111011 periodic orbits corresponding to symbol sequences of length 20 or less, periodic orbits whose symbol sequences have hundreds of symbol...
متن کاملSymbolic dynamics for Lozi maps
We study the family of the Lozi maps La,b : R2 → R2, La,b(x, y) = (1+y−a|x|, bx), and their strange attractors Λa,b. We introduce the set of kneading sequences for the Lozi map and prove that it determines the symbolic dynamics for that map. We also introduce two other equivalent approaches. 2010 Mathematics Subject Classification: 37B10, 37D45, 37E30, 54H20
متن کاملDifferential embedding of the Lorenz attractor.
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: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2014
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004114000061