UsingÉlie Cartan's method of equivalence, we prove an upper bound for the generality of generic rank-1 Bäcklund transformations relating two hyperbolic Monge-Ampère systems. In cases when the Bäcklund transformation admits a symmetry group whose orbits have codimension 1, 2 or 3, we obtain classification results and new examples of auto-Bäcklund transformations.

In this paper, we study the absolute equivalence between Pfaffian systems with a degree 1 independence condition and obtain structural results, particularly for systems of corank 3. We apply these results to understanding dynamic feedback linearization of control systems with 2 inputs.

This paper is concerned with the question: For which pairs of hyperbolic Euler-Lagrange systems in the plane does there exist a rank-1 Bäcklund transformation relating them? We express some obstructions to such existence in terms of the local invariants of the Euler-Lagrange systems. In addition, we discover a class of Bäcklund transformations relating two hyperbolic Euler-Lagrange systems of distinct types.

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To each dynamic equivalence of two control systems is associated an infinite permutation matrix. We investigate how such matrices are related to the existence of dynamic equivalences.