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"Pseudochaotic Kicked Oscillators: Renormalization, Symbolic
Dynamics, and Transport" presents recent developments in
pseudochaos, which is concerned with complex branching behaviors of
dynamical systems at the interface between orderly and chaotic
motion. Pseudochaos is characterized by the trapping of orbits in
the vicinity of self-similar hierarchies of islands of stability,
producing phase-space displacements which increase asymptotically
as a power of time. This monograph is a thorough, self-contained
investigation of a simple one-dimensional model (a kicked harmonic
oscillator) which exhibits pseudochaos in its purest form. It is
intended for graduate students and researchers in physics and
applied mathematics, as well as specialists in nonlinear
dynamics.
Classical dynamics is one of the cornerstones of advanced education in physics and applied mathematics, with applications across engineering, chemistry and biology. In this book, the author uses a concise and pedagogical style to cover all the topics necessary for a graduate-level course in dynamics based on Hamiltonian methods. Readers are introduced to the impressive advances in the field during the second half of the twentieth century, including KAM theory and deterministic chaos. Essential to these developments are some exciting ideas from modern mathematics, which are introduced carefully and selectively. Core concepts and techniques are discussed, together with numerous concrete examples to illustrate key principles. A special feature of the book is the use of computer software to investigate complex dynamical systems, both analytically and numerically. This text is ideal for graduate students and advanced undergraduates who are already familiar with the Newtonian and Lagrangian treatments of classical mechanics. The book is well suited to a one-semester course, but is easily adapted to a more concentrated format of one-quarter or a trimester. A solutions manual and introduction to Mathematica (R) are available online at www.cambridge.org/Lowenstein.
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