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The Restricted Three-Body Problem and Holomorphic Curves

2018-08-29 Mathematics
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Release : 2018-08-29
Genre : Mathematics
Kind : eBook
Book Rating : 786/5 ( reviews)

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Book Synopsis The Restricted Three-Body Problem and Holomorphic Curves by : Urs Frauenfelder

Download or read book The Restricted Three-Body Problem and Holomorphic Curves written by Urs Frauenfelder. This book was released on 2018-08-29. Available in PDF, EPUB and Kindle. Book excerpt: The book serves as an introduction to holomorphic curves in symplectic manifolds, focusing on the case of four-dimensional symplectizations and symplectic cobordisms, and their applications to celestial mechanics. The authors study the restricted three-body problem using recent techniques coming from the theory of pseudo-holomorphic curves. The book starts with an introduction to relevant topics in symplectic topology and Hamiltonian dynamics before introducing some well-known systems from celestial mechanics, such as the Kepler problem and the restricted three-body problem. After an overview of different regularizations of these systems, the book continues with a discussion of periodic orbits and global surfaces of section for these and more general systems. The second half of the book is primarily dedicated to developing the theory of holomorphic curves - specifically the theory of fast finite energy planes - to elucidate the proofs of the existence results for global surfaces of section stated earlier. The book closes with a chapter summarizing the results of some numerical experiments related to finding periodic orbits and global surfaces of sections in the restricted three-body problem. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019

The Three-Body Problem

2012-12-02 Science
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Release : 2012-12-02
Genre : Science
Kind : eBook
Book Rating : 744/5 ( reviews)

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Book Synopsis The Three-Body Problem by : C. Marchal

Download or read book The Three-Body Problem written by C. Marchal. This book was released on 2012-12-02. Available in PDF, EPUB and Kindle. Book excerpt: Recent research on the theory of perturbations, the analytical approach and the quantitative analysis of the three-body problem have reached a high degree of perfection. The use of electronics has aided developments in quantitative analysis and has helped to disclose the extreme complexity of the set of solutions. This accelerated progress has given new orientation and impetus to the qualitative analysis that is so complementary to the quantitative analysis. The book begins with the various formulations of the three-body problem, the main classical results and the important questions and conjectures involved in this subject. The main part of the book describes the remarkable progress achieved in qualitative analysis which has shed new light on the three-body problem. It deals with questions such as escapes, captures, periodic orbits, stability, chaotic motions, Arnold diffusion, etc. The most recent tests of escape have yielded very impressive results and border very close on the true limits of escape, showing the domain of bounded motions to be much smaller than was expected. An entirely new picture of the three-body problem is emerging, and the book reports on this recent progress. The structure of the solutions for the three-body problem lead to a general conjecture governing the picture of solutions for all Hamiltonian problems. The periodic, quasi-periodic and almost-periodic solutions form the basis for the set of solutions and separate the chaotic solutions from the open solutions.

Symplectic Geometry

2022-12-05 Mathematics
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Release : 2022-12-05
Genre : Mathematics
Kind : eBook
Book Rating : 110/5 ( reviews)

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Book Synopsis Symplectic Geometry by : Helmut Hofer

Download or read book Symplectic Geometry written by Helmut Hofer. This book was released on 2022-12-05. Available in PDF, EPUB and Kindle. Book excerpt: Over the course of his distinguished career, Claude Viterbo has made a number of groundbreaking contributions in the development of symplectic geometry/topology and Hamiltonian dynamics. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Holomorphic Curves and Global Questions in Contact Geometry

2019-03-29 Mathematics
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Release : 2019-03-29
Genre : Mathematics
Kind : eBook
Book Rating : 037/5 ( reviews)

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Book Synopsis Holomorphic Curves and Global Questions in Contact Geometry by : Casim Abbas

Download or read book Holomorphic Curves and Global Questions in Contact Geometry written by Casim Abbas. This book was released on 2019-03-29. Available in PDF, EPUB and Kindle. Book excerpt: This book explains the foundations of holomorphic curve theory in contact geometry. By using a particular geometric problem as a starting point the authors guide the reader into the subject. As such it ideally serves as preparation and as entry point for a deeper study of the analysis underlying symplectic field theory. An introductory chapter sets the stage explaining some of the basic notions of contact geometry and the role of holomorphic curves in the field. The authors proceed to the heart of the material providing a detailed exposition about finite energy planes and periodic orbits (chapter 4) to disk filling methods and applications (chapter 9). The material is self-contained. It includes a number of technical appendices giving the geometric analysis foundations for the main results, so that one may easily follow the discussion. Graduate students as well as researchers who want to learn the basics of this fast developing theory will highly appreciate this accessible approach taken by the authors.

The Restricted 3-Body Problem: Plane Periodic Orbits

2011-05-03 Mathematics
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Release : 2011-05-03
Genre : Mathematics
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Book Rating : 730/5 ( reviews)

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Book Synopsis The Restricted 3-Body Problem: Plane Periodic Orbits by : Alexander D. Bruno

Download or read book The Restricted 3-Body Problem: Plane Periodic Orbits written by Alexander D. Bruno. This book was released on 2011-05-03. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

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