Differential Galois Theory and Non-Integrability of Hamiltonian Systems PDF
Preview Differential Galois Theory and Non-Integrability of Hamiltonian Systems
Modern Birkhäuser Classics Juan J. Morales Ruiz Differential Galois Theory and Non-Integrability of Hamiltonian Systems Ferran Sunyer i Balaguer Award winning monograph Modern Birkhäuser Classics Many of the original research and survey monographs in pure and applied mathematics, as well as textbooks, published by Birkhäuser in recent dec- ades have been groundbreaking and have come to be regarded as founda- tional to the subject. Through the MBC Series, a select number of these modern classics, entirely uncorrected, are being re-released in paperback (and as eBooks) to ensure that these treasures remain accessible to new generations of students, scholars, and researchers. Juan J. Morales Ruiz Differential Galois Theory and Non-Integrability of Hamiltonian Systems Reprint of the 1999 Edition Juan J. Morales Ruiz Escuela Superior de Ingenieros de Caminos Canales y Puertos Universidad Politécnica de Madrid Madrid, Spain ISBN 978-3-0348-0720-3 ISBN 978-3-0348-0723-4 (eBook) DOI 10.1007/978-3-0348-0723-4 Springer Basel Heidelberg New York Dordrecht London Library of Congress Control Number: 2013953609 Mathematics Subject Classicfi ation (2010): 12H05, 37J30, 12-02, 32G34, 34C45, 34M15, 34M99, 34Cxx, 34-02, 37J10, 37-02, 58-XX, 70F07, 70H07 © Springer Basel 1999 Reprint of the 1st edition 1999 by Birkhäuser Verlag, Switzerland Originally published as volume 179 in the Progress in Mathematics series This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Cover design: deblik, Berlin Printed on acid-free paper Springer Basel is part of Springer Science+Business Media (www.birkhauser-science.com) Ferran Sunyer i Balaguer 1912–1967 ∗ ∗ ∗ This book has been awarded the Ferran Sunyer i Balaguer 1998 prize. Each year, in honor of the memory of Ferran Sunyer i Balaguer, the Institut d’Estudis Catalans awards an international research prize for a mathematical monographofexpositorynature.Theprize-winningmonographsarepublished in this series. Details about the prize can be found at http://crm.es/info/ffsb.htm Previous winners include – Alexander Lubotzky – M. Ram Murty & V. Kumar Murty Discrete Groups, Expanding Non-vanishing of L-functions Graphs and Invariant Measures and Applications (vol. 157) (vol. 125) – A. B¨ottcher & Yu. I. Karlovich – Klaus Schmidt Carleson Curves, Muckenhoupt Dynamical Systems of Algebraic Weights, and Toeplitz Operators Origin (vol. 128) (vol. 154) Ferran Sunyer i Balaguer 1912–1967 Bornin Figueras(Gerona)with analmostfully incapacitatingphysicaldisability, Ferran Sunyer i Balaguer was confined for all his life to a wheelchair he could not move himself, and was thus constantly dependent on the care of others. His father died when Ferran was two years old, leaving his mother, Angela Balaguer, alonewiththeheavyburdenofnursingherson.Theysubsequentlymovedinwith Ferran’smaternalgrandmotherandhiscousinsMaria,Angeles,andFerran.Later, this exemplaryfamily,which providedtheenvironmentofoverflowingkindnessin which ourfamous mathematician grewup, moved to Barcelona. As the physician thought it advisable to keep the sickly boy away from all sorts of possible strain, such as education and teachers, Ferran was left with the option to learn either by himself or through his mother’s lessons which, thanks toherloveandunderstanding,wereconsideredharmlesstohishealth. Withouta doubt, this education was strongly influenced by his living together with cousins who were to him much more than cousins for all his life. After a period of in- tense reading, arousing a first interest in astronomy and physics, his passion for mathematics emerged and dominated his further life. In 1938, he communicated his first results to Prof. J. Hadamard of the Academy of Sciences in Paris, who published one of his papers in the Academy’s “Comptes Rendus” and encouraged him to proceed in his selected course of in- vestigation. From this moment, Ferran Sunyer i Balaguer maintained a constant interchangewiththeFrenchanalyticalschool,inparticularwithMandelbrojtand his students. In the followingyears,his results were published regularly.The lim- itedspaceheredoesnot,unfortunately,allowforacriticalanalysisofhisscientific achievements. In the mathematical community his work, for which he attained internationalrecognition, is well known. Ferran’sphysicalhandicapdidnotallowhimtowritedownanyofhispapers by himself. He dictated them to his mother until her death in 1955, and when, after a period of grief and desperation, he resumed research with new vigor, his cousins took care of the writing. His working power, paired with exceptional tal- ents,producedanumberofresultswhichwereeventuallyrecognizedfortheirhigh scientific value and for which he was awarded various prizes. These honours not withstanding, it was difficult for him to reachthe socialand professionalposition correspondingtohis scientificachievements.Attimes, his economicsituation was notthemostcomfortableeither.Itwasn’tuntilthe9thofDecember1967,18days prior his death, that his confirmation as a scientific member was made public by the Divisio´n de Ciencias, M´edicas y de Naturaleza of the Council. Furthermore, he waselected only as “de entrada”,in contrastto classmembership. Due to his physical constraints, the academic degrees for his official studies were granted rather belatedly. By the time he was given the Bachelor degree, he hadalreadybeenhonouredbyseveraluniversities!In1960hefinishedhisMaster’s degreeand wasawardedthe doctorateafterthe requisiteperiod oftwoyearsasa student.Althoughhehadbeenapart-timeemployeeoftheMathematicalSeminar FerranSunyeri Balaguer1912–1967 vii since1948,hewasnotallowedtobecomeafullmemberofthescientificstaffuntil 1962. This despite his actually heading the department rather than just being a staff member. HisownpapersregularlyappearedinthejournalsoftheBarcelonaSeminar, Collectanea Mathematica, to which he was also an eminent reviewer and advisor. Onseveraloccasions,hewasconsultedbytheProceedingsoftheAmericanSociety of Mathematics as an advisor. He always participated in and supported guest lecturesinBarcelona,manyofthemhavingbeenpreparedorpromotedbyhim.On the occasionofaconferencein1966,H.MascartofToulousepublicly pronounced his feeling of being honoured by the presence of F. Sunyer i Balaguer, “the first, by far, of Spanish mathematicians”. At all times, Sunyer i Balaguer felt a strong attachment to the scientific activities of his country and modestly accepted the limitations resulting from his attitude, resisting several calls from abroad, in particular from France and some institutions in the USA. In 1963 he was contracted by the US Navy, and in the following years he earned much respect for the results of his investigations. “His valueto the prestigeoftheSpanish scientificcommunitywasoutstandingandhis workinmathematicsofasteadyexcellencethatmakeshislossdifficulttoaccept” (letter ofcondolence fromT.B. Owen, Rear Admiral of the US Navy). Twice, Sunyer i Balaguer was approached by young foreign students who wanted to write their thesis under his supervision, but he had to decline because he was unable to raise the necessary scholarshipmoney. Many times he reviewed doctoralthesesforIndianuniversities,ononeoccasionasthepresidentofadistin- guished international board. The circumstances under which Sunyer attained his scientific achievements also testify to his remarkable human qualities. Indeed, his manner was friendly and his way of conversation reflected his gift for friendship as well as enjoyment of life and work which went far beyond a mere acceptance of the situation into which he had been born. His opinions were as firm as they were cautious, and at the same time he had a deep respect for the opinion and workofothers.Thoughmodestbynature,heachievedduecreditforhiswork,but his petitions werefreeofanytraceofexaggerationorundue self-importance.The most surprising of his qualities was, above all, his absolute lack of preoccupation with his physical condition, which can largely be ascribed to the sensible educa- tion givenby his motherand can be seen asan indicatorofthe integrationofthe disabled into our society. OnDecember27,1967,stillfullyactive,FerranSunyeriBalaguerunexpect- edly passed away.The memory of his remarkablepersonality is a constantsource of stimulation for our own efforts. Translated from Juan Aug´e: Ferran Sunyer Balaguer. Gazeta Matematica, 1.a Serie – Tomo XX – Nums. 3 y 4, 1968,where a complete bibliographycan be found. La panor´amica desde aqu´ı arriba es impresionante. La cara N. de las Buitreras cae a pico sobre el cauce delr´ıoDu´rcalysecontemplalaver- tiente S., escasamente conocida, de los Alayos de Dilar... (Jorge Garzo´n Guti´errez, Andar por Sierra Nevada) To My Father Preface ThisbookisintendedtopresentjointresearchwithmycolleaguesJosep-Maria Peris, Jean-PierreRamis and Carles Simo´. It is strongly based on our original papers but some effort has been made to follow a logical order rather then a historical one. Although the reader should be familiar with the methods of Hamiltonian systems and differential algebra, I have included two review chapters on most of the required material. IlearnedHamiltoniansystemswithCarlesSim´oandthendifferentialGa- lois theory with Jean-Pierre Ramis. They encouraged me to write this mono- graph, read the manuscript and suggested many ways to improve it. I wish to express my deep gratitude to both of them. I would like to thank Josep-Maria Peris for his help and correction of delicate parts of the manuscript. IamverymuchindebtedtotheFerranSunyeriBalaguerFoundationand the Institut d’Estudis Catalans for their support to publish this monograph. Juan J. Morales Ruiz xi
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