This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman Grobman theorem In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations

13 thoughts on “Differential Equations and Dynamical Systems (Texts in Applied Mathematics)”

Good condition except the first nine pages of the first chapter were missing.

Excellent introduction to dynamical systems, combining mathematical rigour and clear explanations It provides a theoretical approach rather than practical implementation of methods.

This text was the assigned text for the first semester of a graduate level mathematical modeling course which I had taken, and it was an incredibly painful book to work with One complaint which I often heard from classmates was the lack of examples in this text Normally, I d think that such a complaint is somewhat invalid for such an advanced level text, as students should be focusing on theory than on specific problems at this stage but the problem here is that the material contained within the text is incredibly weak on the theory and zeroes in on the same boring and uninspiring exercises which are repeated with a new hat in so many sections Theorems are stated in a manner which many people including my own professor, whom actively conducts research in this area found to be incredibly confusing, and a lot of the proofs read like some of the worst hand waving ever, with never ending references to other sources for proofs Rudin sPrinciples of Mathematical Analysisis a popular one which he often refers to, but many times, Perko will skip a detail on a proof and refer to some text which cannot be found in even some of the greatest university libraries To me, it seems ridiculous that a student should go on a wild goose chase to piece together proofs from essentially unavailable sources, when they can actually often be done in a much simpler manner.Unfortunately, even the publisher, Springer which is typically known for only the highest quality products , has truly dropped the ball on this book, by allowing it to be published with typos scattered EVERYWHERE including typos which drastically affect the entire meaning of a theorem Worse is that they have done several reprints of this precise edition of the text, and the typos which were elemented in one reprint may reoccur in the next reprint There was even one occasion where my professor had to provide me with an opportunity to redo an entire assignment, because he was incredibly confused by my results As it turned out, upon going to his office for assistance in the corrections, he noticed that my text had multiple critical typos in a theorem which was to be applied to each exercise, and he had to allow me to borrow his text to copy down the correct information.My main gripe with this book is the exercises Essentially, there is absolutely NO ingenuity or creativity on the exercises, and you essentially end up doing the same small handful of exercises over and over again, just piling on new techniques which are covered in the new section I don t know if repeating exercises over and over again was a deliberate effort to make students feel comfortable with the material as it was repeated, or if it was just sheer laziness But in any event, it really wasn t helpful, and made depending solely upon very basic concepts often ones learned in prerequisite courses rather than what this text should be covering very tempting The worst part is that the exercises presented in the text, as boring and uninspiring as they are, include a ton of elementary busy work, very labor intensive and time consuming, to produce very meaningless results.In all fairness, this is an area of mathematics which is relatively new, and it seems that there haven t quite been any solid standards which have arisen in this area yet But in the meantime, there certainly are some better texts There are several textbooks out there which cover this material, but each one is very unique in the manner in which it presents the material, the essential material needed, and the level of rigor used within Hopefully any standard text which does arise is in no way inspired by this text.

I took an upper level undergraduate graduate class in ODEs and dynamical systems a year ago and it used this textbook Perko is decent introduction to dynamical systems, but it is best used with a few supplementary texts specifically, Smale, Hirsch and Devaney s Differential Equations, Dynamical Systems, and an Introduction to Chaos, and V.I Arnol d s Ordinary Differential Equations I agree with the reviewer who calls it a very good graduate ODEs textbook with some flaws that s generally how I felt about it, too.

This book was required for my class It is a good book if you know the topic and want to use it as a reference Very strong material, but I feel like I could have learned the material better from a friendlier book.But that is opinion based, maybe you ll have better luck I might just be stupid.

This is an assigned text for my graduate level course Overall, I think it is a decent book and covers fair amount of topics, but the impression that I am getting from this book is that it is not written under the presumption that the reader has a strong background in analysis or topology and in that sense it is a tad bit casual in certain definitions My main reservation about this book is that in certain instances the text and sometimes the statements of certain theorems lack clarity and precision, and it takes a rigorous linguistic dissection of the sentences to finally understand what the theorem is saying For a math textbook, this flaw is kind of inexcusable.

I used this book the last two times I taught ordinary differential equations at the graduate level It s a decent book and it covers a lot of topics, but it has an amazing amount of errors, given that it is already in its 3rd edition Some proof techniques I find archaic for example, the insistence on Picard iterations, where a single call to Banach s fixed point theorem would be much clearer A good point are the many exercises, but again, they can contain typos.

the content of the book is outstanding unfortunately the hardcover binding fell off before i even made it through chapter 1 quite disappointing I would return and demand a refund bu I unfortunately need the book on a daily basis for class not sure who printed this, but screwed me over on this one.

I purchased the book new and as soon as I took it out of the box I checked it out and saw that the pages were almost completely coming off the hard cover I was disappointed because it s brand new and unused therefore it should not be falling apart.

Good condition except the first nine pages of the first chapter were missing.

Excellent introduction to dynamical systems, combining mathematical rigour and clear explanations It provides a theoretical approach rather than practical implementation of methods.

Un muy buen libro para el estudio de las ecuacuines diferenciales Muy te rico para aquellos que gustan de las demostraciones.

This book is really frustrating A lot of proofs are omitted, and the reader is constantly referred to other texts for the relevant material.

This text was the assigned text for the first semester of a graduate level mathematical modeling course which I had taken, and it was an incredibly painful book to work with One complaint which I often heard from classmates was the lack of examples in this text Normally, I d think that such a complaint is somewhat invalid for such an advanced level text, as students should be focusing on theory than on specific problems at this stage but the problem here is that the material contained within the text is incredibly weak on the theory and zeroes in on the same boring and uninspiring exercises which are repeated with a new hat in so many sections Theorems are stated in a manner which many people including my own professor, whom actively conducts research in this area found to be incredibly confusing, and a lot of the proofs read like some of the worst hand waving ever, with never ending references to other sources for proofs Rudin sPrinciples of Mathematical Analysisis a popular one which he often refers to, but many times, Perko will skip a detail on a proof and refer to some text which cannot be found in even some of the greatest university libraries To me, it seems ridiculous that a student should go on a wild goose chase to piece together proofs from essentially unavailable sources, when they can actually often be done in a much simpler manner.Unfortunately, even the publisher, Springer which is typically known for only the highest quality products , has truly dropped the ball on this book, by allowing it to be published with typos scattered EVERYWHERE including typos which drastically affect the entire meaning of a theorem Worse is that they have done several reprints of this precise edition of the text, and the typos which were elemented in one reprint may reoccur in the next reprint There was even one occasion where my professor had to provide me with an opportunity to redo an entire assignment, because he was incredibly confused by my results As it turned out, upon going to his office for assistance in the corrections, he noticed that my text had multiple critical typos in a theorem which was to be applied to each exercise, and he had to allow me to borrow his text to copy down the correct information.My main gripe with this book is the exercises Essentially, there is absolutely NO ingenuity or creativity on the exercises, and you essentially end up doing the same small handful of exercises over and over again, just piling on new techniques which are covered in the new section I don t know if repeating exercises over and over again was a deliberate effort to make students feel comfortable with the material as it was repeated, or if it was just sheer laziness But in any event, it really wasn t helpful, and made depending solely upon very basic concepts often ones learned in prerequisite courses rather than what this text should be covering very tempting The worst part is that the exercises presented in the text, as boring and uninspiring as they are, include a ton of elementary busy work, very labor intensive and time consuming, to produce very meaningless results.In all fairness, this is an area of mathematics which is relatively new, and it seems that there haven t quite been any solid standards which have arisen in this area yet But in the meantime, there certainly are some better texts There are several textbooks out there which cover this material, but each one is very unique in the manner in which it presents the material, the essential material needed, and the level of rigor used within Hopefully any standard text which does arise is in no way inspired by this text.

I took an upper level undergraduate graduate class in ODEs and dynamical systems a year ago and it used this textbook Perko is decent introduction to dynamical systems, but it is best used with a few supplementary texts specifically, Smale, Hirsch and Devaney s Differential Equations, Dynamical Systems, and an Introduction to Chaos, and V.I Arnol d s Ordinary Differential Equations I agree with the reviewer who calls it a very good graduate ODEs textbook with some flaws that s generally how I felt about it, too.

This book, is one of the best books in ODE s It include for example the proof od the Hartman Grobman Theorem.

This book was required for my class It is a good book if you know the topic and want to use it as a reference Very strong material, but I feel like I could have learned the material better from a friendlier book.But that is opinion based, maybe you ll have better luck I might just be stupid.

This is an assigned text for my graduate level course Overall, I think it is a decent book and covers fair amount of topics, but the impression that I am getting from this book is that it is not written under the presumption that the reader has a strong background in analysis or topology and in that sense it is a tad bit casual in certain definitions My main reservation about this book is that in certain instances the text and sometimes the statements of certain theorems lack clarity and precision, and it takes a rigorous linguistic dissection of the sentences to finally understand what the theorem is saying For a math textbook, this flaw is kind of inexcusable.

I used this book the last two times I taught ordinary differential equations at the graduate level It s a decent book and it covers a lot of topics, but it has an amazing amount of errors, given that it is already in its 3rd edition Some proof techniques I find archaic for example, the insistence on Picard iterations, where a single call to Banach s fixed point theorem would be much clearer A good point are the many exercises, but again, they can contain typos.

the content of the book is outstanding unfortunately the hardcover binding fell off before i even made it through chapter 1 quite disappointing I would return and demand a refund bu I unfortunately need the book on a daily basis for class not sure who printed this, but screwed me over on this one.

Have had used this text before Very good treatment of global theory Problems are challenging and really make you think.

I purchased the book new and as soon as I took it out of the box I checked it out and saw that the pages were almost completely coming off the hard cover I was disappointed because it s brand new and unused therefore it should not be falling apart.