Chaos: An Introduction for Applied Mathematicians

ISBN-13: 9783030325374 / Angielski / Miękka / 2020 / 303 str.

Andrew Fowler; Mark McGuinness

Recenzje

"The book makes very clear what is and what is not an applied mathematician, arguing that Only a pure mathematician would imagine . . . ,' at least for an applied mathematician . . . ,' and these would not be items of much concern for physicists.'" (Rachel E. Dauncey and Anne C. Skeldon, SIAM Review, Vol. 63 (2), June, 2021)

Spis treści

1 Introduction.- 2 One-Dimensional Maps.- 3 Hopf Bifurcations.- 4 Homoclinic Bifurcations.- 5 Hamiltonian Systems.- 6 Diverse Applications.- Appendix.- References.

O autorze

Andrew Fowler is a Professor of Applied Mathematics at the Universities of Limerick and Oxford.  His principal research interests lie in the applications of mathematics in geoscience.

Mark McGuinness is Professor of Applied Mathematics at Victoria University of Wellington, where he has worked since 1991. He enjoys attending Mathematics-in-Industry Study Groups and working on industrial mathematics problems, as well as modelling geophysical problems using differential equations. He is Chair of ANZIAM and Convenor of the Mathematics in Industry New Zealand Reference Group.

Blurb

This is a textbook on chaos and nonlinear dynamics, written by applied mathematicians for applied mathematicians. It aims to tread a middle ground between the mathematician's rigour and the physicist’s pragmatism.

 

While the subject matter is now classical and can be found in many other books, what distinguishes this book is its philosophical approach, its breadth, its conciseness, and its exploration of intellectual byways, as well as its liberal and informative use of illustration. Written at the graduate student level, the book occasionally drifts from classical material to explore new avenues of thought, sometimes in the exercises. A key feature of the book is its holistic approach, encompassing the development of the subject since the time of Poincaré, and including detailed material on maps, homoclinic bifurcations, Hamiltonian systems, as well as more eclectic items such as Julia and Mandelbrot sets. Some of the more involved codes to produce the figures are described in the appendix.

 

Based on lectures to upper undergraduates and beginning graduate students, this textbook is ideally suited for courses at this level and each chapter includes a set of exercises of varying levels of difficulty.