03330nam a22005295i 4500 978-3-030-59656-9 DE-He213 20251030111359.0 cr nn 008mamaa 240122s2024 sz | s |||| 0|eng d 9783030596569 978-3-030-59656-9 10.1007/978-3-030-59656-9 doi QA370-380 PBKJ bicssc MAT007000 bisacsh PBKJ thema Christopher, Colin. author. aut http://id.loc.gov/vocabulary/relators/aut 69722 Limit Cycles of Differential Equations [electronic resource] / by Colin Christopher, Chengzhi Li, Joan Torregrosa. 2nd ed. 2024. Cham : Springer International Publishing : Imprint: Birkhäuser, 2024. IX, 238 p. 21 illus., 5 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Advanced Courses in Mathematics - CRM Barcelona, 2297-0312 Part 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. This 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. Differential equations. Dynamical systems. Differential Equations. Dynamical Systems. Li, Chengzhi. author. aut http://id.loc.gov/vocabulary/relators/aut 69723 Torregrosa, Joan. author. aut http://id.loc.gov/vocabulary/relators/aut 69724 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783030596552 Printed edition: 9783030596576 Advanced Courses in Mathematics - CRM Barcelona, 2297-0312 69725 https://doi.org/10.1007/978-3-030-59656-9 ZDB-2-SMA ZDB-2-SXMS 57251 57251