000 03330nam a22005295i 4500
001 978-3-030-59656-9
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008 240122s2024 sz | s |||| 0|eng d
020 _a9783030596569
_9978-3-030-59656-9
024 7 _a10.1007/978-3-030-59656-9
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
072 7 _aPBKJ
_2thema
100 1 _aChristopher, Colin.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_969722
245 1 0 _aLimit Cycles of Differential Equations
_h[electronic resource] /
_cby Colin Christopher, Chengzhi Li, Joan Torregrosa.
250 _a2nd ed. 2024.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Birkhäuser,
_c2024.
300 _aIX, 238 p. 21 illus., 5 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aAdvanced Courses in Mathematics - CRM Barcelona,
_x2297-0312
505 0 _aPart I: Around the Center-Focus Problem -- 1 Centers and Limit Cycles -- 2 Darboux Integrability -- 3 Liouvillian Integrability -- 4 Symmetry -- 5 Cherkas’ Systems -- 6 Monodromy -- 7 The Tangential Center-Focus Problem -- 8 Monodromy of Hyperelliptic Abelian Integrals -- 9 Holonomy and the Lotka-Volterra System -- 10 Other Approaches -- Part II: Abelian Integrals and Applications to the Weak Hilbert’s 16th Problem -- 1 Hilbert’s 16th Problem and Its Weak Form -- 2 Abelian Integrals and Limit Cycles -- 3 Estimate of the Number of Zeros of Abelian Integrals -- 4 A Unified Proof of the Weak Hilbert’s 16th Problem for n=2.
520 _aThis textbook contains the lecture series originally delivered at the "Advanced Course on Limit Cycles of Differential Equations" in the Centre de Recerca Matemàtica Barcelona in 2006. The topics covered are the center-focus problem for polynomial vector fields, and the application of Abelian integrals to limit cycle bifurcations. Both topics are related to Hilbert's sixteenth problem. In particular, the book will be of interest to students and researchers working in the qualitative theory of dynamical systems. This second edition provides updates, further clarifications and remarks, and includes an expanded list of references.
650 0 _aDifferential equations.
650 0 _aDynamical systems.
650 1 4 _aDifferential Equations.
650 2 4 _aDynamical Systems.
700 1 _aLi, Chengzhi.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_969723
700 1 _aTorregrosa, Joan.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_969724
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783030596552
776 0 8 _iPrinted edition:
_z9783030596576
830 0 _aAdvanced Courses in Mathematics - CRM Barcelona,
_x2297-0312
_969725
856 4 0 _uhttps://doi.org/10.1007/978-3-030-59656-9
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c57251
_d57251