Displaying similar documents to “On the problem of stability for near to integrable Hamiltonian systems.”

Exponential stability of nonlinear non-autonomous multivariable systems

Michael I. Gil' (2015)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We consider nonlinear non-autonomous multivariable systems governed by differential equations with differentiable linear parts. Explicit conditions for the exponential stability are established. These conditions are formulated in terms of the norms of the derivatives and eigenvalues of the variable matrices, and certain scalar functions characterizing the nonlinearity. Moreover, an estimate for the solutions is derived. It gives us a bound for the region of attraction of the steady...

Stability of periodic waves in Hamiltonian PDEs

Sylvie Benzoni-Gavage, Pascal Noble, L. Miguel Rodrigues (2013)

Journées Équations aux dérivées partielles

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Partial differential equations endowed with a Hamiltonian structure, like the Korteweg–de Vries equation and many other more or less classical models, are known to admit rich families of periodic travelling waves. The stability theory for these waves is still in its infancy though. The issue has been tackled by various means. Of course, it is always possible to address stability from the spectral point of view. However, the link with nonlinear stability  - in fact, stability, since...