國立高雄大學圖資館 |

Limit cycles of differential equations

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Limit cycles of differential equationsby Colin Christopher, Chengzhi Li, Joan Torregrosa.
作者:	Christopher, Colin.
其他作者:	Li, Chengzhi.
出版者:	Cham :Springer International Publishing :2024.
面頁冊數:	ix, 238 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Limit cycles.
電子資源:	https://doi.org/10.1007/978-3-030-59656-9
ISBN:	9783030596569$q(electronic bk.)

Limit cycles of differential equations
Christopher, Colin.

Limit cycles of differential equations[electronic resource] /by Colin Christopher, Chengzhi Li, Joan Torregrosa. - Second edition. - Cham :Springer International Publishing :2024. - ix, 238 p. :ill., digital ;24 cm. - Advanced courses in mathematics - CRM Barcelona,2297-0312. - Advanced courses in mathematics - CRM Barcelona..

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.

ISBN: 9783030596569$q(electronic bk.)

Standard No.: 10.1007/978-3-030-59656-9doiSubjects--Topical Terms:

561851
Limit cycles.

LC Class. No.: QA371 / .C56 2024

Dewey Class. No.: 515.35

Limit cycles of differential equations
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505 0 $a 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.
520 $a 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.
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