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- Boris Kruglikov, Valentin Lychagin
- 2008

We study the equivalence problem of submanifolds with respect to a transitive pseudogroup action. The corresponding differential invariants are determined via formal theory and lead to the notions of l-variants and l-covariants, even in the case of non-integrable pseudogroup. Their calculation is based on the cohomological machinery: We introduce a complex… (More)

- BORIS KRUGLIKOV, VALENTIN LYCHAGIN
- 2005

For the Spencer δ-cohomologies of a symbolic system we construct a spectral sequence associated with a subspace. We calculate the sequence for the systems of Cohen-Macaulay type and obtain a reduction theorem, which facilitates computation of δ-cohomologies by reducing dimension of the system. Using this algebraic result we prove an efficient compatibility… (More)

The problem of local feedback equivalence for 1-dimensional control systems of the 1-st order is considered. The algebra of differential invari-ants and criteria for the feedback equivalence for regular control systems are found.

- Maks A. Akivis, Vladislav V. Goldberg, Valentin V. Lychagin
- 2008

We find d − 2 relative differential invariants for a d-web, d ≥ 4, on a two-dimensional manifold and prove that their vanishing is necessary and sufficient for a d-web to be linearizable. If one writes the above invariants in terms of web functions f (x, y) and g4(x, y), ..., g d (x, y), then necessary and sufficient conditions for the linearizabilty of a… (More)

- Vladislav V. Goldberg, Valentin V. Lychagin
- 2008

We find relative differential invariants of orders eight and nine for a planar nonparallelizable 3-web such that their vanishing is necessary and sufficient for a 3-web to be linearizable. This solves the Blaschke conjecture for 3-webs. As a side result, we show that the number of linearizations in the Gronwall conjecture does not exceed fifteen and give… (More)

- Boris Kruglikov, Valentin Lychagin
- 2008

We establish an efficient compatibility criterion for a system of generalized complete intersection type in terms of certain multi-brackets of differential operators. These multi-brackets generalize the higher Jacobi-Mayer brackets, important in the study of evolutionary equations and the integrability problem. We also calculate Spencer δ-cohomology of… (More)

- Vladislav V. Goldberg, Valentin V. Lychagin
- 2006

We find an invariant characterization of planar webs of maximum rank. For 4-webs, we prove that a planar 4-web is of maximum rank three if and only if it is linearizable and its curvature vanishes. This result leads to the direct web-theoretical proof of the Poincaré's theorem: a planar 4-web of maximum rank is linearizable. We also find an invariant… (More)

- V Lychagin
- 1993

- BORIS KRUGLIKOV, VALENTIN LYCHAGIN
- 2006

We discuss the dimensional characterization of the solutions space of a formally integrable system of partial differential equations and provide certain formulas for calculations of these dimensional quantities.

- Boris Kruglikov, Valentin Lychagin
- 2005

We generalize the notion of involutivity to systems of differential equations of different orders and show that the classical results relating invo-lutivity, restrictions, characteristics and characteristicity, known for first order systems, extend to the general context. This involves, in particular, a new definition of strong characteristicity. The proof… (More)