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This work brings together previously unpublished notes contributed by participants of the IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence (Moscow, 25-30 August 2006). The study of vortex motion is of great interest to fluid and gas dynamics: since all real flows are vortical in nature, applications of the vortex theory are extremely diverse, many of them (e.g. aircraft dynamics, atmospheric and ocean phenomena) being especially important.
With a pedagogic format ideal for graduate students, this text includes a wealth of examples focusing on solutions in dynamical systems theory that mirror those used in Lyapunov's first method, tackling ordinary differential equations expressed as series form.
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