Dynamics: The Geometry Of Behavior by Ralph H. Abraham (PDF)

Description

Dynamics: The Geometry of Behavior (Studies in Nonlinearity)

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐At a recent AMA conference, over 500 applied mathematicians in fields as far ranging as chemistry and psychology voted Dynamical Systems Theory (DST) among the top three “most important applications of mathematics” in the past 100 years.This isn’t to slight relativity or quantum physics, it is more to acknowledge the role of DST IN those fields, as well as Neurology, Cognition, Neuron Firing, Traffic Flows, Ecology, Engineering, Chemistry, Biology, and hundreds of other disciplines.Many scientifically savvy lay folks, and even many applied scientists, associate DST with Chaos Theory, Lagrangians in physics, and ODE/PDE applications to cyclical systems like the “rabbit vs. the coyote” population system. When you survey books about DST today, there was a whole “crop” 15 years ago on cognition and neurology, yet today’s texts and courses emphasize linear algebra and differential equations, often giving either lip or no service to the geometry which is at the heart of DST.Abraham’s Geometry of Behavior series was originally planned to be a five volume set explicitly designed to cover DST VISUALLY, with as little symbolic math as possible, to give students a real intuitive feel for the geometry and inner meaning of saddle points, attractors and repellors, characteristic exponents, chaos, oscillation and much more. Four of the five volumes were eventually published, with the fifth (Manifolds and Mappings) remaining a scholarly monograph/ outline.The four volumes that made it (1. Periodic/ linear behavior; 2. Chaotic behavior; 3. Global behavior; and 4. Bifurcation behavior) were roughly organized around increasing dimensions of DST as well as increasing difficulty, with the first volume being the foundation for all four. Volume one centers on limit sets, pendulums and thus foundational periodic limit cycles. Volume two covers dependence on initial conditions and details Poincaire, Rossler, Lorenz and Birkoff. Three develops the “whole picture” with fractals, multiple attractors, basins, etc. Finally, four contains encyclopedic coverage of changes resulting from changes in control parameters.All four texts are filled with over 100 pages of detailed, two color line drawings that make the central points mentioned above, WITHOUT using formulas. I’m not saying you can learn DST without formulas, but these explanations and line drawing give “ahas” page after page on what lies beneath all the formulas, to give a unique intuition on what the formulas are trying to convey. Parabolic exponents suddenly become swirling 2 and 3D spirals, characteristics become points on the intersecting real/imaginary axis, transforms are wonderfully seen as overlay coordinates turning to align with attractors, and MUCH more.The first volume of this incredible series is becoming very hard to find, and thus very expensive, but some Amazon third parties still have full sets at below the price of the first volume, yet including it! Not many folks would suggest DST for High School students today given the removal of discrete math, linear algebra and certainly differential equations from curricula, yet this series gives teachers the opportunity to introduce the topic painlessly.Also ideally suited for self study, and even serious DST friendly applied math grads and engineers looking for a little better understanding of the underlying geometry. I work on animating math, and it is not intuitive to watch a pendulum converge on a disappearing attractor and imagine a spiral instead of a sine or “normal” curve. UNTIL you see this book’s “higher dimension” pendulum spinning in a circle around that same point that reduces to the point AS a spiral. As fun as it is educational, filled with many memorable “I now get it” moments. Highly Recommended.

⭐This books is unique, certainly in dynamical systems but most likely in all of math: there are no equations so you can’t use it as a textbook BUT it is the must have companion to other dynamical systems books (Strogatz, Wiggins, Verhulst, Hirsch-Smale-Devaney etc…).Clear a labor of love, it consists of hundreds of pages of hand-drawn figures illustrating the geometry in 1,2,3D dynamical systems.I see as the flag bearer to Poincare-Smale-Arnold view of mathematics.

⭐This is an outstanding and inimitable book on dynamics. Essentially, it is an extensive illustrated guide with very little text, lots of historical remarks and almost no symbolic mathematics (just an appendix at the end). The book covers a lot of concepts and the many charts and drawings succeed in illuminating otherwise complicated ideas. Note that you will not learn dynamics from this book alone but it is definitely the perfect companion for more abstract texts stressing on the conceptual, symbolic and computational aspects of dynamics. It is regrettable that this gem is hard to get now but it is worth to get a good used copy. It will certainly add many ours of intellectual joy to your studies in dynamics. Highly recommendable!

⭐This is a wonderful guide to nonlinear dynamical systems. Abraham and Shaw emphasize visual over verbal representations of mathematical and dynamical concepts. Some may find the lack of exhaustive text to be a limitation, but I found the visually-based approach to nonlinear dynamic systems to be concise, appealing, and effective.

⭐This is truly a book for the 21st century. This review can merely add to what has already been said by other reviewers. The book introduces in an intuitive but really thorough way the subject of dynamics. It is telling that the title includes the term “behavior”. The strength of this book lies, for me, in the way in which it demonstrates, using sets of compelling and beautifully drawn illustrations, how dynamic systems behave, what they do, as time and other dimensions change. It tells you visually what happens and why! Books like this are rare (and valuable). I bought my copy of the second edition in 1993.For me, it is a perfect companion to another favorite book of mine, “The Arrow of Time” by Coveney and Highfield.

⭐By far the best graphic introduction to nonlinear dynamics

⭐I’ve been looking for this book (I was familiar with the 1982 4 volume version) for over a decade since I last put it back on the library shelf, moved, and never could find it again.This is an absolutely unique book carefully crafted to give the reader an intuition for what the differential equations actually mean. If only it weren’t so expensive!

⭐This is one of my favorite books. Chock full of enlightening artwork, page after page of colorful drawings, graphs, representations of springs, sound, heat, and other non-linear, real-world phenomena explained and illustrated for intuitive ease. Even if you’re not a scientist, or a mathematics fan – this book will open your eyes to concepts that scientists deal with, and that deeply inspire artists and musicians alike.It’s a little like learning chess, and realizing that almost everything is like chess.Everything is dynamics!

⭐Das mir zugesandte Büchlein zeigt wie zu erwarten ein paar Spuren der Zeit (ein sympathisches Eselsohr) und einen Namenseintrag des Vorbesitzers.Soweit zum Äußeren des Buches. Der Inhalt ist faszinierend und war mir schon vom Studium her bekannt. Die Grundzüge der modernen Theorie der dynamischen Systeme werden klar dargestellt mit vielen Bildern und erklärendem Text. Auf symbolische Darstellungen, wie in der Mathematik sonst üblich, wird systematisch verzichtet, um den Inhalt einer breiten Bevölkerungsschicht vorzustellen.Dieses Buch soll – laut Vorwort – ein Versuch sein, Mathematik in anderen wissenschaftlichen Disziplinen zu verankern. Es ist erschreckend wie ärmlich andere Disziplinen der Wissenschaft von der Mathematik geprägt sind.Als Physiker muss ich doch behaupten, dass wir uns sehr um die Mathematik bemühen. Trotzdem ist dieses Buch auch Physikern zu empfehlen,Manuel

⭐

Keywords

Free Download Dynamics: The Geometry Of Behavior in PDF format
Dynamics: The Geometry Of Behavior PDF Free Download
Download Dynamics: The Geometry Of Behavior 2015 PDF Free
Dynamics: The Geometry Of Behavior 2015 PDF Free Download
Download Dynamics: The Geometry Of Behavior PDF
Free Download Ebook Dynamics: The Geometry Of Behavior