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Overview"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." Full Product DetailsAuthor: Colin Christopher , Chengzhi Li , Joan TorregrosaPublisher: Springer Nature Switzerland AG Imprint: Springer Nature Switzerland AG Edition: 2nd ed. 2024 Weight: 0.426kg ISBN: 9783030596552ISBN 10: 3030596559 Pages: 238 Publication Date: 23 January 2024 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsAround the Center-Focus Problem.- Centers and Limit Cycles.- Darboux Integrability.- Liouvillian Integrability.- Symmetry.- Cherkas’ Systems.- Monodromy.- The Tangential Center-Focus Problem.- Monodromy of Hyperelliptic Abelian Integrals.- Holonomy and the Lotka-Volterra System.- Other Approaches.- Abelian Integrals and Applications to the Weak Hilbert’s 16th Problem.- Hilbert’s 16th Problem and Its Weak Form.- Abelian Integrals and Limit Cycles.- Estimate of the Number of Zeros of Abelian Integrals.- A Unified Proof of the Weak Hilbert’s 16th Problem for n=2.ReviewsAuthor InformationColin Christopher is Associate Head of School at the University of Plymouth in Devon, UK.Chengzhi Li is Professor Emeritus at the Peking University in China. Joan Torregrosa is Associate Professor at the Universitat Autònoma de Barcelona in Bellaterra, Spain. Tab Content 6Author Website:Countries AvailableAll regions |
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