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See the FAQ. Also I am not sure why the OP wanted a dynamical-systems tag on this question. For the time being I'll leave it there. AaronS 1 1 silver badge 8 8 bronze badges. Dick Palais Dick Palais Sign up or log in Sign up using Google. Sign up using Facebook.

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Marsden and M. Integration and Differential Equations by R. Johnson, , pp, 3. Introduction to Differential Equations by Jeff.

Chasnov, , pages, 1. Evans, , pages, 1. Piette, , 89 pages, KB, PS. Causon, C.

Exterior Differential Systems and Euler-Lagrange Partial Differential Equations - Download link

Mingham, , pages, 4. Lectures on Differential Equations by Craig A. Varadhan, , pp, 1. Lectures on Exterior Differential Systems by M. Lectures on Partial Differential Equations by G.

Harrell II, James V. Herod, For example, in a river where the current is faster in midstream it turns out that downstream geodesics are stable, but that upstream geodesics are not. The geometric quantity that measures this notion of stability is known as 'curvature', since it was first identified in studies of the curvature of the Earth. Bryant's work studies curvature and 'over-determined' systems of differential equations, and is relevant to optimization problems in motion planning, control theory, robotics, and string theory models in high energy physics.

Robert L. Bryant Phillip A. Griffiths Dan Grossman.

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A review of some geometric integrators

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