The parameterization method for invariant manifolds : from rigorous results to effective computations

• 作者： Haro, Alex, author.
• 其他作者：
  • Canadell, Marta, author.
  • Figueras, Jordi-Lluis, author.
  • Luque, Alejandro, author.
  • Mondelo, Josep Maria, author.
  • SpringerLink (Online service)
• 其他題名：
  • Applied mathematical sciences ;
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： Applied mathematical sciences,volume 195
• 主題： Invariant manifolds. , Mathematics. , Dynamical Systems and Ergodic Theory. , Statistical Physics, Dynamical Systems and Complexity. , Numerical Analysis. , Partial Differential Equations.
• ISBN： 9783319296623 (electronic bk.) 、 9783319296609 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: An Overview of the Parameterization Method for Invariant Manifolds -- Seminumerical Algorithms for Computing Invariant Manifolds of Vector Fields at Fixed Points -- The Parameterization Method for Quasi-Periodic Systems: From Rigorous Results to Validated Numerics -- The Parameterization Method in KAM Theory -- A Newton-like Method for Computing Normally Hyperbolic Invariant Tori.
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• 摘要註: This monograph presents some theoretical and computational aspects of the parameterization method for invariant manifolds, focusing on the following contexts: invariant manifolds associated with fixed points, invariant tori in quasi-periodically forced systems, invariant tori in Hamiltonian systems and normally hyperbolic invariant manifolds. This book provides algorithms of computation and some practical details of their implementation. The methodology is illustrated with 12 detailed examples, many of them well known in the literature of numerical computation in dynamical systems. A public version of the software used for some of the examples is available online. The book is aimed at mathematicians, scientists and engineers interested in the theory and applications of computational dynamical systems.
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