Titlebook: Asymptotics beyond All Orders; Harvey Segur,Saleh Tanveer,Herbert Levine Book 1991 Springer Science+Business Media New York 1991 Renormali

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Helen Parkhurst and the Dalton School,Patterns formed by the instabilities in propagating interfaces between different phases have received much attention. in recent years. One of the well known examples is the Saffman-Taylor problem in a Hele-Shaw cell., where an unique finger pattern is observed when a viscous fluid is displaced by a less viscous fluid.

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Marietta Johnson and the Organic School,The rapidly forced pendulum equation with forcing δ sin t/ε, where δ = δ. ε., p = 5, for δ., ε sufficiently small, is considered. We sketch our proof that stable and unstable manifolds split and that the splitting distance d(t.) in the ?-t plane satisfies.and the angle of transversal intersection, ψ, in the t = 0 section satisfies ..

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https://doi.org/10.1007/978-1-137-05475-3This paper concerns with the split of a separatrix of a nonlinear pendulum by a small but rapid sinsusoidal forcing. A partial answer is given, with main result, road map and proof of δ-asymptotic expansion.

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https://doi.org/10.1007/978-94-007-1848-7The solutions of the equation . are discussed in the limit as ε → 0. This equation arises as a connection problem in the theory of resonant oscillations in a tank..

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Michael J. Munkert,Klaus KüspertThis paper generalizes the Pokrovskii-Khalatnikov method to calculate the actual behavior of the reflection coefficient for singular problems, which vanishes to all orders in the small parameter e. Two different classes of reflection coefficient problems are considered.

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