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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

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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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Titre: | ## Shadowing in Dynamical Systems: Theory and Applications |

ISBN: |

** Informations détaillées sur le livre - Shadowing in Dynamical Systems: Theory and Applications**

EAN (ISBN-13): 9780792361794

ISBN (ISBN-10): 0792361792

Version reliée

Date de parution: 2000

Editeur: SPRINGER VERLAG GMBH

316 Pages

Poids: 0,621 kg

Langue: eng/Englisch

Livre dans la base de données depuis 18.01.2007 14:57:02

Livre trouvé récemment le 16.12.2016 13:30:00

ISBN/EAN: 0792361792

ISBN - Autres types d'écriture:

0-7923-6179-2, 978-0-7923-6179-4

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