A First Course In Dynamics

The theory of dynamical systems is a major mathematical discipline closely intertwined with all main areas of mathematics. It has greatly stimulated research in many sciences and given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introduction for senior undergraduate and beginning graduate students of mathematics, physics, and engineering combines mathematical rigor with copious examples of important applications. It covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. Readers need not be familiar with manifolds or measure theory; the only prerequisite is a basic undergraduate analysis course. The authors begin by describing the wide array of scientific and mathematical questions that dynamics can address. They then use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. The final chapters introduce modern developments and applications of dynamics. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAM-theory.

The theory of dynamical systems has given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introductory text covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. The only prerequisite is a basic undergraduate analysis course. The authors use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAM-theory.

The theory of dynamical systems has given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introductory text covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. The only prerequisite is a basic undergraduate analysis course. The authors use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAM-theory.

This exciting text provides a mathematically rigorous yet accessible textbook that is primarily aimed at atmospheric science majors. Its accessibility is due to the texts emphasis on conceptual understanding. The first five chapters constitute a companion text to introductory courses covering the dynamics of the mid-latitude atmosphere. The final four chapters constitute a more advanced course, and provide insights into the diagnostic power of the quasi-geostrophic approximation of the equations outlined in the previous chapters, the meso-scale dynamics of thefrontal zone, the alternative PV perspective for cyclone interpretation, and the dynamics of the life-cycle of mid-latitude cyclones. Written in a clear and accessible style Features real weather examples and global case studies Each chapter sets out clear learning objectives and tests students’ knowledge with concluding questions and answers A Solutions Manual is also available for this textbook on the Instructor Companion Site www.wileyeurope.com/college/martin. “...a student-friendly yet rigorous textbook that accomplishes what no other textbook has done before... I highly recommend this textbook. For instructors, this is a great book if they don’t have their own class notes – one can teach straight from the book. And for students, this is a great book if they don’t take good class notes – one can learn straight from the book. This is a rare attribute of advanced textbooks.” Bulletin of the American Meteorological Society (BAMS), 2008

Given the ease with which computers can do iteration it is now possible for almost anyone to generate beautiful images whose roots lie in discrete dynamical systems. Images of Mandelbrot and Julia sets abound in publications both mathematical and not. The mathematics behind the pictures are beautiful in their own right and are the subject of this text. Mathematica programs that illustrate the dynamics are included in an appendix.

This book introduces the subject of fluid dynamics from the first principles.

This book provides a broad coverage of computational fluid dynamics that will interest engineers, astrophysicists, mathematicians, oceanographers and ecologists.

A First Course in Chaotic Dynamical Systems: Theory and Experiment is the first book to introduce modern topics in dynamical systems at the undergraduate level. Accessible to readers with only a background in calculus, the book integrates both theory and computer experiments into its coverage of contemporary ideas in dynamics. It is designed as a gradual introduction to the basic mathematical ideas behind such topics as chaos, fractals, Newton's method, symbolic dynamics, the Julia set, and the Mandelbrot set, and includes biographies of some of the leading researchers in the field of dynamical systems. Mathematical and computer experiments are integrated throughout the text to help illustrate the meaning of the theorems presented.Chaotic Dynamical Systems Software, Labs 1–6 is a supplementary laboratory software package, available separately, that allows a more intuitive understanding of the mathematics behind dynamical systems theory. Combined with A First Course in Chaotic Dynamical Systems, it leads to a rich understanding of this emerging field.