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Scalar differential invariants of symplectic Monge-Ampère equations

100%

Paris A., Vinogradov A.

Open Mathematics

2011

tom 9

nr 4

731-751

All second order scalar differential invariants of symplectic hyperbolic and elliptic Monge-Ampère equations with respect to symplectomorphisms are explicitly computed. In particular, it is shown that the number of independent second order invariants is equal to 7, in sharp contrast with general Monge-Ampère equations for which this number is equal to 2. We also introduce a series of invariant differential forms and vector fields which allow us to construct numerous scalar differential invariants of higher order. The introduced invariants give a solution of the symplectic equivalence of Monge-Ampère equations. As an example we study equations of the form u xy + f(x, y, u x, u y) = 0 and in particular find a simple linearization criterion.

Integrable systems and group actions

75%

Miranda E.

Open Mathematics

2014

tom 12

nr 2

240-270

The main purpose of this paper is to present in a unified approach to different results concerning group actions and integrable systems in symplectic, Poisson and contact manifolds. Rigidity problems for integrable systems in these manifolds will be explored from this perspective.

Ograniczanie wyników

2 Open Mathematics

1 Miranda E.

1 Paris A.

1 Vinogradov A.

1 2014

1 2011

Wyniki wyszukiwania

Scalar differential invariants of symplectic Monge-Ampère equations

Integrable systems and group actions