Arnold: Swimming Against the Tide by Boris A. Khesin, Serge L. Tabachnikov

By Boris A. Khesin, Serge L. Tabachnikov

Vladimir Arnold, an eminent mathematician of our time, is understood either for his mathematical effects, that are many and trendy, and for his robust evaluations, usually expressed in an uncompromising and inspiring demeanour. His dictum that "Mathematics is part of physics the place experiments are reasonable" is widely known. This e-book comprises elements: chosen articles by means of and an interview with Vladimir Arnold, and a suite of articles approximately him written by way of his buddies, colleagues, and scholars. The booklet is generously illustrated by means of a wide number of photos, a few by no means earlier than released. The publication offers many an aspect of this impressive mathematician and guy, from his mathematical discoveries to his daredevil outdoors adventures.

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I hope that this Encyclopædia is useful as the source describing the real origins of mathematical ideas and methods (see, for instance, my paper on the catastrophe theory in vol. 5). Unfortunately, in the Library FROM HILBERT’S SUPERPOSITION PROBLEM TO DYNAMICAL SYSTEMS 29 of Congress, and hence in all the USA libraries, the volumes of the Encyclopædia of Mathematical Sciences are scattered according to the author/subject alphabetical order, which makes its use as an encyclopædia extremely difficult.

You have the fast phase oscillations in a system, like a pendulum, located at a point of the surface. You slowly move the point along the surface, and the direction of the pendulum oscillations is parallel transported according to the LeviCivita connection. I think this is the most physical way to define the Levi-Civita connection which otherwise is mathematically a rather complicated thing in higher dimensions. The adiabatic transportation defines it as a physically natural object. I think this can’t be found in any textbook, I only find this in Klein.

According to Radon, the Levi-Civita connection can be defined by the adiabatic invariants theory. You have the fast phase oscillations in a system, like a pendulum, located at a point of the surface. You slowly move the point along the surface, and the direction of the pendulum oscillations is parallel transported according to the LeviCivita connection. I think this is the most physical way to define the Levi-Civita connection which otherwise is mathematically a rather complicated thing in higher dimensions.

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