Titlebook: Infinite Dimensional Dynamical Systems; John Mallet-Paret,Jianhong Wu,Huaiping Zhu Book 2013 Springer Science+Business Media New York 2013

先行

A Simple Proof of the Stability of Solitary Waves in the Fermi-Pasta-Ulam Model Near the KdV Limit, limit we give a simple proof that small amplitude, long-wavelength solitary waves in the Fermi-Pasta-Ulam (FPU) model are linearly stable and hence by the results of Friesecke and Pego that they are also nonlinearly, asymptotically stable.

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中和

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John Mallet-Paret,Jianhong Wu,Huaiping ZhuIncludes the last paper co-authored by legendary dynamist Jack Hale, and honors legendary scientist George Sell, who has contributed to the subject for several decades.Discusses cutting-edge developme

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Fields Institute Communicationshttp://image.papertrans.cn/i/image/464622.jpg

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Instability of Radially-Symmetric Spikes in Systems with a Conserved Quantity,We show that radially symmetric spikes are unstable in a class of reaction-diffusion equations coupled to a conservation law.

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Littlewood Problem for a Singular Subquadratic Potential,We consider a periodically forced singular oscillator in which the potential has subquadratic growth at infinity and admits a singularity. Using Moser’s twist theorem of invariant curves, we show the existence of quasiperiodic solutions. This solves the Littlewood problem on the boundedness of all solutions for such a system.

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Differential Equations with Random Delay,The Multiplicative Ergodic Theorem by Oseledets on Lyapunov spectrum and Oseledets subspaces is extended to linear random differential equations with random delay, using a recent result by Lian and Lu. Random differential equations with bounded delay are discussed as an example.