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ISBN: 9780792361794
In this book the theory of hyperbolic sets is developed, both for diffeomorphisms and flows, with an emphasis on shadowing. We show that hyperbolic sets are expansive and have the shadowing property. Then we use shadowing to prove that hyperbolic sets are robust under perturbation, that they have an asymptotic phase property and also that the dynamics near a transversal homoclinic orbit is chaotic. It turns out that chaotic dynamical systems arising in practice are not quite hyperbolic. However, they possess enough hyperbolicity to enable us to use shadowing ideas to give computer-assisted proofs that computed orbits of such systems can be shadowed by true orbits for long periods of time, that they possess periodic orbits of long periods and that it is really true that they are chaotic. Audience: This book is intended primarily for research workers in dynamical systems but could also be used in an advanced graduate course taken by students familiar with calculus in Banach spaces and with the basic existence theory for ordinary differential equations. Textbooks New Books ~~ Mathematics~~ Differential Equations ~~ General Shadowing-in-Dynamical-Systems~~KJ-Palmer Springer US In this book the theory of hyperbolic sets is developed, both for diffeomorphisms and flows, with an emphasis on shadowing. We show that hyperbolic sets are expansive and have the shadowing property. Then we use shadowing to prove that hyperbolic sets are robust under perturbation, that they have an asymptotic phase property and also that the dynamics near a transversal homoclinic orbit is chaotic. It turns out that chaotic dynamical systems arising in practice are not quite hyperbolic. However, they possess enough hyperbolicity to enable us to use shadowing ideas to give computer-assisted proofs that computed orbits of such systems can be shadowed by true orbits for long periods of time, that they possess periodic orbits of long periods and that it is really true that they are chaotic. Audience: This book is intended primarily for research workers in dynamical systems but could also be used in an advanced graduate course taken by students familiar with calculus in Banach spaces and with the basic existence theory for ordinary differential equations.
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ISBN: 9780792361794
ID: 6387116
In this book the theory of hyperbolic sets is developed, both for diffeomorphisms and flows, with an emphasis on shadowing. We show that hyperbolic sets are expansive and have the shadowing property. Then we USE shadowing to prove that hyperbolic sets are robust under perturbation, that they have an asymptotic phase property and also that the dynamics near a transversal homoclinic orbit is In this book the theory of hyperbolic sets is developed, both for diffeomorphisms and flows, with an emphasis on shadowing. We show that hyperbolic sets are expansive and have the shadowing property. Then we USE shadowing to prove that hyperbolic sets are robust under perturbation, that they have an asymptotic phase property and also that the dynamics near a transversal homoclinic orbit is chaotic. It turns out that chaotic dynamical systems arising in practice are not quite hyperbolic. However, they possess enough hyperbolicity to enable us to USE shadowing ideas to give computer-assisted proofs that computed orbits of such systems can be shadowed by true orbits for long periods of time, that they possess periodic orbits of long periods and that it is really true that they are chaotic. Audience: This book is intended primarily for research workers in dynamical systems but could also be used in an advanced graduate course taken by students familiar with calculus in Banach spaces and with the basic existence theory for ordinary differential equations. Books, Science and Geography~~Mathematics~~Calculus & Mathematical Analysis, Shadowing In Dynamical Systems~~Book~~9780792361794~~K.H. Palmer, , , , , , , , , ,, [PU: Kluwer Academic Publishers]
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ISBN: 9780792361794
ID: 5dac794a9191eb51d0c217c6b275dcda
Theory and Applications In this book the theory of hyperbolic sets is developed, both for diffeomorphisms and flows, with an emphasis on shadowing. We show that hyperbolic sets are expansive and have the shadowing property. Then we use shadowing to prove that hyperbolic sets are robust under perturbation, that they have an asymptotic phase property and also that the dynamics near a transversal homoclinic orbit is chaotic. It turns out that chaotic dynamical systems arising in practice are not quite hyperbolic. However, they possess enough hyperbolicity to enable us to use shadowing ideas to give computer-assisted proofs that computed orbits of such systems can be shadowed by true orbits for long periods of time, that they possess periodic orbits of long periods and that it is really true that they are chaotic. Audience: This book is intended primarily for research workers in dynamical systems but could also be used in an advanced graduate course taken by students familiar with calculus in Banach spaces and with the basic existence theory for ordinary differential equations. Bücher / Fremdsprachige Bücher / Englische Bücher 978-0-7923-6179-4, Springer
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ISBN: 9780792361794
ID: 106277065
In this book the theory of hyperbolic sets is developed, both for diffeomorphisms and flows, with an emphasis on shadowing. We show that hyperbolic sets are expansive and have the shadowing property. Then we use shadowing to prove that hyperbolic sets are robust under perturbation, that they have an asymptotic phase property and also that the dynamics near a transversal homoclinic orbit is chaotic. It turns out that chaotic dynamical systems arising in practice are not quite hyperbolic. However, they possess enough hyperbolicity to enable us to use shadowing ideas to give computer-assisted proofs that computed orbits of such systems can be shadowed by true orbits for long periods of time, that they possess periodic orbits of long periods and that it is really true that they are chaotic. Audience: This book is intended primarily for research workers in dynamical systems but could also be used in an advanced graduate course taken by students familiar with calculus in Banach spaces and with the basic existence theory for ordinary differential equations. Theory and Applications Buch (fremdspr.) Bücher>Fremdsprachige Bücher>Englische Bücher, Springer
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ISBN: 9780792361794
ID: 9780792361794
In this book the theory of hyperbolic sets is developed, both for diff eomorphisms and flows, with an emphasis on shadowing. We show that hyp erbolic sets are expansive and have the shadowing property. Then we us e shadowing to prove that hyperbolic sets are robust under perturbatio n, that they have an asymptotic phase property and also that the dynam ics near a transversal homoclinic orbit is chaotic. Textbooks New, Books~~Mathematics~~Differential Equations~~General, Shadowing-in-Dynamical-Systems~~KJ-Palmer, 999999999, Shadowing in Dynamical Systems: Theory and Applications, K.J. Palmer, 0792361792, Springer US, , , , , Springer US
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Title: | Shadowing in Dynamical Systems: Theory and Applications |
ISBN: | 9780792361794 |
Details of the book - Shadowing in Dynamical Systems: Theory and Applications
EAN (ISBN-13): 9780792361794
ISBN (ISBN-10): 0792361792
Hardcover
Publishing year: 2000
Publisher: SPRINGER VERLAG GMBH
316 Pages
Weight: 0,621 kg
Language: eng/Englisch
Book in our database since 18.01.2007 14:57:02
Book found last time on 16.12.2016 13:30:00
ISBN/EAN: 9780792361794
ISBN - alternate spelling:
0-7923-6179-2, 978-0-7923-6179-4
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