the topology of chaos alice in stretch and squeezeland pdf

The topology of chaos alice in stretch and squeezeland pdf

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The topology of chaos : Alice in stretch and squeezeland

Computational Mechanics Reader

Visualizing global manifolds during the transition to chaos in the Lorenz system

A highly valued resource for those who wish to move from the introductory and preliminary understandings and the measurement of chaotic behavior to a more.

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The topology of chaos : Alice in stretch and squeezeland

If one wants to study the global dynamics of a given system, key com ponents are the stable or unstable manifolds of invariant sets, such as equilibria and periodic orbits. Even in the simplest examples, these global manifolds must be approximated by means of numerical computations. We discuss an algorithm for computing global manifolds of vector fields that is decidedly geometric in nature. A two-dimensional manifold is built up as a collection of approximate geodesic level sets, i. Our method allows to visualize the resulting surface by making use of the geodesic parametrization. As we show with the example of the Lorenz system, this is a big advantage when one wants to understand the geometry of complicated two-dimensional global man ifolds.

Jetzt bewerten Jetzt bewerten. A highly valued resource for those who wish to move from the introductory and preliminary understandings and the measurement of chaotic behavior to a more sophisticated and precise understanding of chaotic systems. The authors provide a deep understanding of the structure of strange attractors, how they are classified, and how the information required to identify and classify a strange attractor can be extracted from experimental data. In its first edition, the Topology of Chaos has been a valuable resource for physicist and mathematicians interested in the topological analysis of dynamical …mehr. DE Als Download kaufen. Jetzt verschenken.

Computational Mechanics Reader

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A highly valued resource for those who wish to move from the introductory and preliminary understandings and the measurement of chaotic behavior to a more.


Visualizing global manifolds during the transition to chaos in the Lorenz system

A blender is a hyperbolic set with a stable or unstable invariant manifold that behaves as a geometric object of a dimension larger than that of the respective manifold itself. Blenders have been constructed in diffeomorphisms with a phase space of dimension at least three. We consider here the question of how one can identify, characterize and also visualize the underlying hyperbolic set of a given diffeomorphism to verify whether it actually is a blender or not. This allows to determine and illustrate whether the hyperbolic set is a blender; in particular, we consider as a distinguishing feature the self-similar structure of the intersection set of the respective global invariant manifold with a plane. By checking and illustrating a denseness property, we are able to identify a parameter range over which the hyperbolic set is a blender, and we discuss and illustrate how the blender disappears.

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The Topology of Chaos: Alice in Stretch and Squeezeland

Улочка начала сужаться. - Soccoro! - Его голос звучал еле слышно.  - Помогите.

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