We consider a class of Hamiltonian systems with linear potential, elastic constraints and arbitrary number of degrees of freedom. We establish sufficient conditions for complete hyperbolicity of the system.
We consider a class of flows which includes both magnetic flows and Gaussian thermostats of external fields. We give sufficient conditions for such flows on manifolds of negative sectional curvature to be Anosov.
We give a simple direct proof of the polar decomposition for separated linear maps in pseudo-Euclidean geometry.
My statement is "tangent" to the discussion of applied mathematics. I refer to the opinion of the prof. Bialynicki-Birula (2014) about the importance of teaching mathematics. I hope to learn from you about the teaching of higher mathematics non-mathematicians in your university. I see this on a big threat to the maintenance of the level and scope of mathematical research in Poland.
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