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An Exploration of Dynamical Systems and Chaos: Completely by John H. Argyris, Gunter Faust, Maria Haase, Rudolf Friedrich PDF

By John H. Argyris, Gunter Faust, Maria Haase, Rudolf Friedrich

ISBN-10: 3662460416

ISBN-13: 9783662460412

ISBN-10: 3662460424

ISBN-13: 9783662460429

This booklet is conceived as a entire and targeted text-book on non-linear dynamical structures with specific emphasis at the exploration of chaotic phenomena. The self-contained introductory presentation is addressed either to people who desire to examine the physics of chaotic platforms and non-linear dynamics intensively in addition to those people who are curious to benefit extra concerning the attention-grabbing global of chaotic phenomena. uncomplicated techniques like Poincaré part, iterated mappings, Hamiltonian chaos and KAM conception, unusual attractors, fractal dimensions, Lyapunov exponents, bifurcation concept, self-similarity and renormalisation and transitions to chaos are completely defined. To facilitate comprehension, mathematical ideas and instruments are brought briefly sub-sections. The textual content is supported through quite a few laptop experiments and a mess of graphical illustrations and color plates emphasising the geometrical and topological features of the underlying dynamics.

This quantity is a totally revised and enlarged moment version which contains lately got learn result of topical curiosity, and has been prolonged to incorporate a brand new part at the simple techniques of chance conception. a very new bankruptcy on totally built turbulence provides the successes of chaos idea, its boundaries in addition to destiny tendencies within the improvement of advanced spatio-temporal buildings.

"This ebook can be of precious aid for my lectures" Hermann Haken, Stuttgart

"This text-book shouldn't be lacking in any introductory lecture on non-linear systems

and deterministic chaos" Wolfgang Kinzel, Würzburg

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Additional resources for An Exploration of Dynamical Systems and Chaos: Completely Revised and Enlarged Second Edition

Sample text

Where the non-linear vector function F (x Thus, the introduction of additional variables transforms the non-autonomous eq. 8) with second-order derivatives with respect to time into a system of three first-order differential equations. 3). The phase portrait of eq. 9) for the variables x1 , x˙ 1 shows intersecting trajectories corresponding to specific choices of control parameters and initial conditions (fig. 4). Trajectories of the autonomous type of eq. 9) which do not intersect in the extended phase space with the coordinates x1 , x˙ 1 and t do so in the projection onto the (x, x)-plane, ˙ the customary phase space.

An extensive discussion of these concepts can be found in the context of dissipative systems and attractors in Chapter 5. The examples of mechanical systems mentioned here make it clear that the concept of the attractor plays a central role in the description of the behaviour of damped systems subject to deterministic equations of motion. We basically differentiate between two types: regular attractors and strange attractors. On the one hand, there are three classic types of motion: equilibrium, periodic motion and quasiperiodic motion.

In this highly simplified statement, we share the view of Max Born (1959) who says that absolute accuracy is not a physically meaningful concept and can only be found in the conceptual world of mathematicians. Felix Klein called for the application of “approximation mathematics” side by side with the usual “precision mathematics”. Since his suggestion remained without response at the time, the physicists at the turn of the preceding century solved their problems in their own conceptual framework, using methods of probability and statistical laws.

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An Exploration of Dynamical Systems and Chaos: Completely Revised and Enlarged Second Edition by John H. Argyris, Gunter Faust, Maria Haase, Rudolf Friedrich

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