Central Configurations Periodic Orbits And Hamiltonian Systems

Author : Jaume Llibre,Richard Moeckel,Carles Simó
Publisher : Birkhäuser
Page : 232 pages
File Size : 47,7 Mb
Release : 2015-12-18
Category : Mathematics
ISBN : 9783034809337

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Central Configurations, Periodic Orbits, and Hamiltonian Systems by Jaume Llibre,Richard Moeckel,Carles Simó Pdf

The notes of this book originate from three series of lectures given at the Centre de Recerca Matemàtica (CRM) in Barcelona. The first one is dedicated to the study of periodic solutions of autonomous differential systems in Rn via the Averaging Theory and was delivered by Jaume Llibre. The second one, given by Richard Moeckel, focusses on methods for studying Central Configurations. The last one, by Carles Simó, describes the main mechanisms leading to a fairly global description of the dynamics in conservative systems. The book is directed towards graduate students and researchers interested in dynamical systems, in particular in the conservative case, and aims at facilitating the understanding of dynamics of specific models. The results presented and the tools introduced in this book include a large range of applications.

Author : Lacomba Ernesto A,Llibre Jaume
Publisher : #N/A
Page : 408 pages
File Size : 55,9 Mb
Release : 1996-07-03
Category : Electronic
ISBN : 9789814547901

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New Trends For Hamiltonian Systems And Celestial Mechanics by Lacomba Ernesto A,Llibre Jaume Pdf

This volume puts together several important lectures on the Hamiltonian Systems and Celestial Mechanics to form a comprehensive and authoritative collection of works on the subject. Their relationship to several aspects of topology, mechanics and dynamical systems in general are also emphasized. The papers presented are an outgrowth of the lectures that took place during the “International Symposium on Hamiltonian Systems and Celestial Mechanics ”, which was held at Cocoyoc (Morelos, México) from September 13 to 17, 1994.

Author : J Delgado,E A Lacomba,E Pérez-Chavela,J Llibre
Publisher : World Scientific
Page : 370 pages
File Size : 51,7 Mb
Release : 2000-10-09
Category : Science
ISBN : 9789814492119

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Hamiltonian Systems and Celestial Mechanics by J Delgado,E A Lacomba,E Pérez-Chavela,J Llibre Pdf

This volume is an outgrowth of the Third International Symposium on Hamiltonian Systems and Celestial Mechanics. The main topics are Arnold diffusion, central configurations, singularities in few-body problems, billiards, area-preserving maps, and geometrical mechanics. All papers in the volume went through the refereeing process typical of a mathematical research journal. Contents:The Rhomboidal Charged Four Body Problem (F Alfaro & E Pérez-Chavela)Planetary Rings with Shepherds (L Benet & T H Seligman)Low Reynolds Number Swimming in Two Dimensions (A Cherman et al.)2-Dimensional Invariant Tori for the Spatial Isosceles 3-Body Problem (M Corbera & J Llibre)The Global Flow for the Synodical Spatial Kepler Problem (M P Dantas & J Llibre)Unbounded Growth of Energy in Periodic Perturbations of Geodesic Flows of the Torus (A Delshams et al.)Splitting and Melnikov Potentials in Hamiltonian Systems (A Delshams & P Gutiérrez)Infinity Manifolds of Cubic Polynomial Hamiltonian Vector Fields with 2 Degrees of Freedom (M Falconi et al.)Relativistic Corrections to Elementary Galilean Dynamics and Deformations of Poisson Brackets (R Flores-Espinoza & Y M Vorobjev)Heteroclinic Phenomena in the Sitnikov Problem (A García & E Pérez-Chavela)Doubly-Symmetric Periodic Solutions of Hill's Lunar Problem (R C Howison & K R Meyer)On Practical Stability Regions for the Motion of a Small Particle Close to the Equilateral Points of the Real Earth-Moon System (À Jorba)Variational Methods for Quasi-Periodic Solutions of Partial Differential Equations (R de la Llave)The Splitting of Invariant Lagrangian Submanifolds: Geometry and Dynamics (J-P Marco)Cross-Sections in the Planar N-Body Problem (C McCord)Existence of an Additional First Integral and Completeness of the Flow for Hamiltonian Vector Fields (J Muciño-Raymundo)Simplification of Perturbed Hamiltonians Through Lie Transformations (J Palacián & P Yanguas)Linear Stability in the 1 + N-Gon Relative Equilibrium (G E Roberts)Analytic Continuation of Circular and Elliptic Kepler Motion to the General 3-Body Problem (J Soler)The Phase Space of Finite Systems (K B Wolf et al.) Readership: Students and researchers in mathematics and nonlinear dynamics. Keywords:Charged Four Body Problem;Low Reynolds Number;Relativistic Corrections;Sitnikov Problem;Hill's Lunar Problem;Invariant Lagrangian Submanifolds;Planar N-Body Problem;Elliptic Kepler Motion

Author : Joaquín Delgado,Ernesto A. Lacomba,Jaume Llibre,Ernesto Perez-Chavela
Publisher : Springer Science & Business Media
Page : 261 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781441990587

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New Advances in Celestial Mechanics and Hamiltonian Systems by Joaquín Delgado,Ernesto A. Lacomba,Jaume Llibre,Ernesto Perez-Chavela Pdf

The aim of the IV International Symposium on Hamiltonian Systems and Celestial Mechanics, HAMSYS-2001 was to join top researchers in the area of Celestial Mechanics, Hamiltonian systems and related topics in order to communicate new results and look forward for join research projects. For PhD students, this meeting offered also the opportunity of personal contact to help themselves in their own research, to call as well and promote the attention of young researchers and graduated students from our scientific community to the above topics, which are nowadays of interest and relevance in Celestial Mechanics and Hamiltonian dynamics. A glance to the achievements in the area in the last century came as a consequence of joint discussions in the workshop sessions, new problems were presented and lines of future research were delineated. Specific discussion topics included: New periodic orbits and choreographies in the n-body problem, singularities in few body problems, central configurations, restricted three body problem, geometrical mechanics, dynamics of charged problems, area preserving maps and Arnold diffusion.

Author : Montserrat Corbera,Josep Maria Cors,Jaume Llibre,Andrei Korobeinikov
Publisher : Birkhäuser
Page : 160 pages
File Size : 53,8 Mb
Release : 2015-10-20
Category : Mathematics
ISBN : 9783319221298

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Extended Abstracts Spring 2014 by Montserrat Corbera,Josep Maria Cors,Jaume Llibre,Andrei Korobeinikov Pdf

The two parts of the present volume contain extended conference abstracts corresponding to selected talks given by participants at the "Conference on Hamiltonian Systems and Celestial Mechanics 2014" (HAMSYS2014) (15 abstracts) and at the "Workshop on Virus Dynamics and Evolution" (12 abstracts), both held at the Centre de Recerca Matemàtica (CRM) in Barcelona from June 2nd to 6th, 2014, and from June 23th to 27th, 2014, respectively. Most of them are brief articles, containing preliminary presentations of new results not yet published in regular research journals. The articles are the result of a direct collaboration between active researchers in the area after working in a dynamic and productive atmosphere. The first part is about Central Configurations, Periodic Orbits and Hamiltonian Systems with applications to Celestial Mechanics – a very modern and active field of research. The second part is dedicated to mathematical methods applied to viral dynamics and evolution. Mathematical modelling of biological evolution currently attracts the interest of both mathematicians and biologists. This material offers a variety of new exciting problems to mathematicians and reasonably inexpensive mathematical methods to evolutionary biologists. It will be of scientific interest to both communities. The book is intended for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active areas of research.

Author : Kenneth Meyer,Glen Hall,Dan Offin
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 44,8 Mb
Release : 2008-12-05
Category : Mathematics
ISBN : 9780387097244

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Introduction to Hamiltonian Dynamical Systems and the N-Body Problem by Kenneth Meyer,Glen Hall,Dan Offin Pdf

Arising from a graduate course taught to math and engineering students, this text provides a systematic grounding in the theory of Hamiltonian systems, as well as introducing the theory of integrals and reduction. A number of other topics are covered too.

Author : Anonim
Publisher : World Scientific
Page : 380 pages
File Size : 50,6 Mb
Release : 2000
Category : Mathematics
ISBN : 9810244630

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Hamiltonian Systems and Celestial Mechanics by Anonim Pdf

This volume is an outgrowth of the Third International Symposium on Hamiltonian Systems and Celestial Mechanics. The main topics are Arnold diffusion, central configurations, singularities in few-body problems, billiards, area-preserving maps, and geometrical mechanics. All papers in the volume went through the refereeing process typical of a mathematical research journal.

Author : Donald Saari,Alain Chenciner,Richard H. Cushman,Clark Robinson,Zhihong Jeff Xia
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 51,7 Mb
Release : 2002
Category : Celestial mechanics
ISBN : 9780821829028

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Celestial Mechanics by Donald Saari,Alain Chenciner,Richard H. Cushman,Clark Robinson,Zhihong Jeff Xia Pdf

This volume reflects the proceedings from an international conference on celestial mechanics held at Northwestern University (Evanston, IL) in celebration of Donald Saari's sixtieth birthday. Many leading experts and researchers presented their recent results. Don Saari's significant contribution to the field came in the late 1960s through a series of important works. His work revived the singularity theory in the $n$-body problem which was started by Poincare and Painleve. Saari'ssolution of the Littlewood conjecture, his work on singularities, collision and noncollision, on central configurations, his decompositions of configurational velocities, etc., are still much studied today and were reflected throughout the conference. This volume covers various topics of currentresearch, from central configurations to stability of periodic orbits, from variational methods to diffusion mechanisms, from the dynamics of secular systems to global dynamics of the solar systems via frequency analysis, from Hill's problem to the low energy transfer orbits and mission design in space travel, and more. This classic field of study is very much alive today and this volume offers a comprehensive representation of the latest research results.

Author : Donald Saari,Zhihong Xia
Publisher : American Mathematical Soc.
Page : 252 pages
File Size : 44,5 Mb
Release : 1996
Category : Mathematics
ISBN : 0821855344

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Hamiltonian Dynamics and Celestial Mechanics by Donald Saari,Zhihong Xia Pdf

This book contains selected papers from the AMS-IMS-SIAM Joint Summer Conference on Hamiltonian Systems and Celestial Mechanics held in Seattle in June 1995. The symbiotic relationship of these two topics creates a natural combination for a conference on dynamics. Topics covered include twist maps, the Aubrey-Mather theory, Arnold diffusion, qualitative and topological studies of systems, and variational methods, as well as specific topics such as Melnikov's procedure and the singularity properties of particular systems. As one of the few books that addresses both Hamiltonian systems and celestial mechanics, this volume offers emphasis on new issues and unsolved problems. Many of the papers give new results, yet the editors purposely included some exploratory papers based on numerical computations, a section on unsolved problems, and papers that pose conjectures while developing what is known.

Author : Hansjörg Geiges
Publisher : Cambridge University Press
Page : 241 pages
File Size : 52,9 Mb
Release : 2016-03-24
Category : Mathematics
ISBN : 9781107125407

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The Geometry of Celestial Mechanics by Hansjörg Geiges Pdf

A first course in celestial mechanics emphasising the variety of geometric ideas that have shaped the subject.

Author : Stephen Lynch
Publisher : Birkhäuser
Page : 585 pages
File Size : 52,7 Mb
Release : 2017-10-12
Category : Mathematics
ISBN : 9783319614854

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Dynamical Systems with Applications Using Mathematica® by Stephen Lynch Pdf

This book provides an introduction to the theory of dynamical systems with the aid of the Mathematica® computer algebra package. The book has a very hands-on approach and takes the reader from basic theory to recently published research material. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks. Theorems and proofs are kept to a minimum. The first section deals with continuous systems using ordinary differential equations, while the second part is devoted to the study of discrete dynamical systems.

Author : Vlad Bally,Lucia Caramellino,Rama Cont
Publisher : Birkhäuser
Page : 208 pages
File Size : 52,7 Mb
Release : 2016-03-11
Category : Mathematics
ISBN : 9783319271286

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Stochastic Integration by Parts and Functional Itô Calculus by Vlad Bally,Lucia Caramellino,Rama Cont Pdf

This volume contains lecture notes from the courses given by Vlad Bally and Rama Cont at the Barcelona Summer School on Stochastic Analysis (July 2012). The notes of the course by Vlad Bally, co-authored with Lucia Caramellino, develop integration by parts formulas in an abstract setting, extending Malliavin's work on abstract Wiener spaces. The results are applied to prove absolute continuity and regularity results of the density for a broad class of random processes. Rama Cont's notes provide an introduction to the Functional Itô Calculus, a non-anticipative functional calculus that extends the classical Itô calculus to path-dependent functionals of stochastic processes. This calculus leads to a new class of path-dependent partial differential equations, termed Functional Kolmogorov Equations, which arise in the study of martingales and forward-backward stochastic differential equations. This book will appeal to both young and senior researchers in probability and stochastic processes, as well as to practitioners in mathematical finance.

Author : Jürgen Moser
Publisher : American Mathematical Soc.
Page : 87 pages
File Size : 48,6 Mb
Release : 1968
Category : Celestial mechanics
ISBN : 9780821812815

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Lectures on Hamiltonian Systems by Jürgen Moser Pdf

Author : Alessandro Colombo,Mike Jeffrey,J. Tomàs Lázaro,Josep M. Olm
Publisher : Birkhäuser
Page : 193 pages
File Size : 51,8 Mb
Release : 2017-05-24
Category : Science
ISBN : 9783319556420

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Extended Abstracts Spring 2016 by Alessandro Colombo,Mike Jeffrey,J. Tomàs Lázaro,Josep M. Olm Pdf

This volume contains extended abstracts outlining selected talks and other selected presentations given by participants throughout the "Intensive Research Program on Advances in Nonsmooth Dynamics 2016", held at the Centre de Recerca Matemàtica (CRM) in Barcelona from February 1st to April 29th, 2016. They include brief research articles reporting new results, descriptions of preliminary work or open problems, and outlines of prominent discussion sessions. The articles are all the result of direct collaborations initiated during the research program. The topic is the theory and applications of Nonsmooth Dynamics. This includes systems involving elements of: impacting, switching, on/off control, hybrid discrete-continuous dynamics, jumps in physical properties, and many others. Applications include: electronics, climate modeling, life sciences, mechanics, ecology, and more. Numerous new results are reported concerning the dimensionality and robustness of nonsmooth models, shadowing variables, numbers of limit cycles, discontinuity-induced bifurcations and chaos, determinacy-breaking, stability criteria, and the classification of attractors and other singularities. This material offers a variety of new exciting problems to mathematicians, but also a diverse range of new tools and insights for scientists and engineers making use of mathematical modeling and analysis. The book is intended for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active areas of research.

Author : Kenneth Meyer,Glen Hall
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 43,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475740738

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Introduction to Hamiltonian Dynamical Systems and the N-Body Problem by Kenneth Meyer,Glen Hall Pdf

The theory of Hamiltonian systems is a vast subject which can be studied from many different viewpoints. This book develops the basic theory of Hamiltonian differential equations from a dynamical systems point of view. That is, the solutions of the differential equations are thought of as curves in a phase space and it is the geometry of these curves that is the important object of study. The analytic underpinnings of the subject are developed in detail. The last chapter on twist maps has a more geometric flavor. It was written by Glen R. Hall. The main example developed in the text is the classical N-body problem, i.e., the Hamiltonian system of differential equations which describe the motion of N point masses moving under the influence of their mutual gravitational attraction. Many of the general concepts are applied to this example. But this is not a book about the N-body problem for its own sake. The N-body problem is a subject in its own right which would require a sizable volume of its own. Very few of the special results which only apply to the N-body problem are given.