SØG - mellem flere end 8 millioner bøger:
Viser: Limit Cycles of Differential Equations
Limit Cycles of Differential Equations
Colin Christopher, Chengzhi Li og Joan Torregrosa
(2024)
Sprog: Engelsk
om ca. 10 hverdage
Detaljer om varen
- 2. Udgave
- Paperback
- Udgiver: Springer International Publishing AG (Januar 2024)
- Forfattere: Colin Christopher, Chengzhi Li og Joan Torregrosa
- ISBN: 9783030596552
This textbook contains the lecture series originally delivered at the "Advanced Course on Limit Cycles of Differential Equations" in the Centre de Rechercha Mathematica Barcelona in 2006. It covers the center-focus problem for polynomial vector fields and the application of abelian integrals to limit cycle bifurcations. Both topics are related to the authors' interests in Hilbert's sixteenth problem, but would also be of interest to those working more generally in the qualitative theory of dynamical systems.
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.