{"product_id":"shadowing-in-dynamical-systems-theory-and-applications-von-k-j-palmer","title":"Shadowing in Dynamical Systems","description":"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.  \u003cbr\u003e  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. \u003cbr\u003e  \u003cem\u003eAudience:\u003c\/em\u003e 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.\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9781441948274\"\u003e\u003ch3\u003eTheory and Applications\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9781441948274","offer_id":39415528357981,"sku":"9781441948274","price":106.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/8cbb0551-18fe-40ac-acb6-026d4fe3d893.jpg?v=1772170891","url":"https:\/\/shop.autorenwelt.de\/products\/shadowing-in-dynamical-systems-theory-and-applications-von-k-j-palmer","provider":"Autorenwelt Shop","version":"1.0","type":"link"}