In recent years, due primarily to the proliferation of computers, dynamical systems has again returned to its roots in applications. It is the aim of this book to provide undergraduate and beginning graduate students in mathematics or science and engineering with a modest foundation of knowledge. Equations in dimensions one and two constitute the majority of the text, and in particular it is demonstrated that the basic notion of stability and bifurcations of vector fields are easily explained for scalar autonomous equations. Further, the authors investigate the dynamics of planar autonomous equations where new dynamical behavior, such as periodic and homoclinic orbits appears.
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J.K. Hale, H. Kocak, and H. Buttanri Dynamics and Bifurcations "This book takes the reader step by step through the vast subject of dynamical systems. Proceeding from 1 to 2 dimensions and onto higher dimensions in separate self-contained sections, the text is mathematically rigorous yet devoid of excess formalism. A refreshing balance is further achieved by the use of many excellent illustrations and a wealth of worked and unworked examples."—MATHEMATIKA
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16 of 16 people found the following review helpful:
5.0 out of 5 stars
A great introduction to dynamical systems,
This review is from: Dynamics and Bifurcations (Texts in Applied Mathematics, Vol. 3) (Hardcover)
As a postgrad student searching for textbooks to cover all those things I learnt about dynamical systems in my undergrad studies, this one was one of my first choices. It is easy to read, which is surprising, considering it's a maths textbook. It is systematic in its treatment of dynamical systems. The important things are easy to find, since the index is very comprehensive and the layout of the page makes formulae stand out. The many diagrams help those of us who think about dynamics geometrically. All in all, a great book, which I use on a regular basis as a reference.
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This review is from: Dynamics and Bifurcations (Texts in Applied Mathematics, Vol. 3) (Hardcover)
This books succeeds as an introduction to Dynamics and Bifurcations. It has lot's of great pictures and examples. The authors really did a great job in that respect.Some of the theorems could be described a bit clearer, particularly the ones about Poincare-Hopf-Andronov bifurcations.
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This review is from: Dynamics and Bifurcations (Texts in Applied Mathematics, Vol. 3) (Hardcover)
This is one of the most inspired books on the subject of dynamical systems.It has a straight argument, with a very comprehensive text and one may even find it some times poetic. Yes, I do love and recomend it!
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First Sentence:
In this introductory section we establish our notation for differential equations and their solutions. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
structurally unstable vector fields, nonhyperbolic linear map, scalar autonomous differential equations, stable orbit structure, quadratic degeneracy, cubic degeneracy, planar differential equations, planar linear systems, corresponding conservative system, principal matrix solution, hyperbolic linear systems, delayed logistic map, nonhyperbolic equilibrium point, first unit square, nonhyperbolic fixed point, nonhyperbolic equilibria, asymptotically stable periodic orbit, structurally stable vector fields, heteroclinic saddle connection, transversal homoclinic points, homoclinic loop, nontrivial periodic orbit, representative phase portraits, same orbit structure, invariant cylinder Key Phrases - Capitalized Phrases (CAPs): (learn more)
Implicit Function Theorem, Jordan Normal Form, Bibliographical Notes, Twist Theorem, Continuation of Example, Mean Value Theorem, Flow Box Theorem, Jordan Curve Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this introductory section we establish our notation for differential equations and their solutions. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
structurally unstable vector fields, nonhyperbolic linear map, scalar autonomous differential equations, stable orbit structure, quadratic degeneracy, cubic degeneracy, planar differential equations, planar linear systems, corresponding conservative system, principal matrix solution, hyperbolic linear systems, delayed logistic map, nonhyperbolic equilibrium point, first unit square, nonhyperbolic fixed point, nonhyperbolic equilibria, asymptotically stable periodic orbit, structurally stable vector fields, heteroclinic saddle connection, transversal homoclinic points, homoclinic loop, nontrivial periodic orbit, representative phase portraits, same orbit structure, invariant cylinder Key Phrases - Capitalized Phrases (CAPs): (learn more)
Implicit Function Theorem, Jordan Normal Form, Bibliographical Notes, Twist Theorem, Continuation of Example, Mean Value Theorem, Flow Box Theorem, Jordan Curve Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 80
books:
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100
books
cite this book:
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- Morse Theory (Annals of Mathematic Studies AM-51) by John Milnor on page 440, and Back Matter
- Differential equations: An introduction by David A Sanchez in Back Matter (1), and Back Matter (2)
- Differential Equations (with CD-ROM) by Paul Blanchard in Back Matter (1), and Back Matter (2)
- Dynamical Systems: Valparaiso 1986 : Proceedings of a Symposium Held in Valparaiso (Lecture Notes in Mathematics) by R. Bamon in Back Matter (1), and Back Matter (2)
- Ordinary Differential Equations (Universitext) by Vladimir I. Arnold in Back Matter
See all 80 books this book cites
- From Nonlinearity to Coherence: Universal Features of Non-linear Behaviour in Many-Body Physics (Oxford Science Publications) by J. M. Dixon on page 69, and page 299
- Bifurcation and Chaos in Complex Systems, Volume 1 (Edited Series on Advances in Nonlinear Science and Complexity) by Jian-Qiao Sun Ph.D. M.S. B.S. on page 276, and page 336
- An Introduction to Nonlinear Partial Differential Equations by J. David Logan on page 182, and Back Matter
- Introduction to Perturbation Methods by Mark H. Holmes in Front Matter, and Back Matter
- Differential Equations: A Dynamical Systems Approach. Part II: Higher Dimensional Systems (Texts in Applied Mathematics) (Pt. 2) by John H. Hubbard in Front Matter, and page 521
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