Global Properties of Linear Ordinary Differential Equations by Frantisek NeumanGlobal Properties of Linear Ordinary Differential Equations by Frantisek Neuman

Global Properties of Linear Ordinary Differential Equations

byFrantisek Neuman

Paperback | November 13, 2013

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This monograph contains a description of original methods and results concern­ ing global properties of linear differential equations of the nth order, n <_20_22c_20_and20_summarizes20_results20_in20_this20_field20_in20_a20_unified20_fashion.20_however2c_20_this20_monoc2ad_20_graph20_is20_by20_no20_means20_intended20_to20_be20_a20_survey20_of20_all20_results20_in20_this20_area.20_i20_t20_contains20_only20_a20_selection20_of20_results2c_20_which20_serves20_to20_illustrate20_the20_unified20_approach20_presented20_here.20_by20_using20_recent20_methods20_and20_results20_of20_algebra2c_20_topology2c_20_differential20_geometry2c_20_functional20_analysis2c_20_theory20_of20_functional20_equations20_and20_linear20_differential20_equations20_of20_the20_second20_order2c_20_and20_by20_introducing20_several20_original20_methods2c_20_global20_solutions20_of20_problems20_which20_were20_previously20_studied20_only20_locally20_by20_kummer2c_20_brioschi2c_20_laguerre2c_20_forsyth2c_20_halphen2c_20_lie2c_20_stiickel20_and20_others20_are20_provided.20_the20_structure20_of20_global20_transformations20_is20_described20_by20_algebraic20_means20_28_theory20_of20_categories3a_20_brandt20_and20_ehresmann20_groupoids29_2c_20_a20_new20_geometrical20_approach20_is20_introduced20_that20_leads20_to20_global20_canonical20_forms20_28_in20_contrast20_to20_the20_local20_laguerre-forsyth20_or20_halphen20_forms29_20_and20_is20_suitable20_for20_the20_application20_of20_cartan27_27_s20_moving-frame-of-reference20_method. _22c_="" and="" summarizes="" results="" in="" this="" field="" a="" unified="" fashion.="" _however2c_="" _monoc2ad_="" graph="" is="" by="" no="" means="" intended="" to="" be="" survey="" of="" all="" area.="" i="" t="" contains="" only="" selection="" _results2c_="" which="" serves="" illustrate="" the="" approach="" presented="" here.="" using="" recent="" methods="" _algebra2c_="" _topology2c_="" differential="" _geometry2c_="" functional="" _analysis2c_="" theory="" equations="" linear="" second="" _order2c_="" introducing="" several="" original="" _methods2c_="" global="" solutions="" problems="" were="" previously="" studied="" locally="" _kummer2c_="" _brioschi2c_="" _laguerre2c_="" _forsyth2c_="" _halphen2c_="" _lie2c_="" stiickel="" others="" are="" provided.="" structure="" transformations="" described="" algebraic="" _28_theory="" _categories3a_="" brandt="" ehresmann="" _groupoids29_2c_="" new="" geometrical="" introduced="" that="" leads="" canonical="" forms="" _28_in="" contrast="" local="" laguerre-forsyth="" or="" halphen="" _forms29_="" suitable="" for="" application="" _cartan27_27_s="" moving-frame-of-reference="">
Title:Global Properties of Linear Ordinary Differential EquationsFormat:PaperbackDimensions:320 pagesPublished:November 13, 2013Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9401050570

ISBN - 13:9789401050579

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Table of Contents

Series Editors Preface. Preface. Symbols defined in the text. 1. Introduction with historical remarks. 2. Notation, definitions and some basic facts. 3. Global transformations. 4. Analytic, algebraic and geometrical aspects of global transformations. 5. Criterion of global equivalence. 6. Stationary groups. 7. Canonical forms. 8. Invariants. 9. Equations with solutions of prescribed properties. 10. Zeros of solutions. 11. Related results and some applications. 12. Appendix: Two functional equations. Literature cited in the book and/or for supplementary reading. Subject index. Index of names.