Browsing by Author "Lychagin, Valentin V."

Abelian equations and rank problems for planar webs
Lychagin, Valentin V.; Goldberg, Vladislav V. (Journal article; Tidsskriftartikkel; Peer reviewed, 20060504)We find an invariant characterization of planar webs of maximum rank. For 4webs, we prove that a planar 4web is of maximum rank three if and only if it is linearizable and its curvature vanishes. This result leads ... 
The categorical theory of relations and quantization
Lychagin, Valentin V.; Jakobsen, Per K. (Working paper; Arbeidsnotat, 20011030)In this paper we develops a categorical theory of relations and use this formulation to define the notion of quantization for relations. Categories of relations are defined in the context of symmetric monoidal categories. They ... 
Compatibility, multibrackets and integrability of systems of PDEs
Kruglikov, Boris; Lychagin, Valentin V. (Journal article; Tidsskriftartikkel; Peer reviewed, 20080220)We establish an efficient compatibility criterion for a system of generalized complete intersection type in terms of certain multibrackets of differential operators. These multibrackets generalize the higher Jacobi Mayer ... 
Differential invariants of the motion group actions
Kruglikov, Boris; Lychagin, Valentin V. (Working paper; Arbeidsnotat, 20071220)Differential invariants of a (pseudo)group action can vary when restricted to invariant submanifolds (differential equations). The algebra is still governed by the LieTresse theorem, but may change a lot. We describe ... 
Dimension of the solutions space of PDEs
Kruglikov, Boris; Lychagin, Valentin V. (Conference object; Konferansebidrag, 20061026)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. 
Feedback Differential Invariants
Lychagin, Valentin V. (Journal article; Tidsskriftartikkel, 20081207)The problem of feedback equivalence for control systems is considered. An algebra of differential invariants and criteria for the feedback equivalence for regular control systems are found. 
Feedback Equivalence of 1dimensional Control Systems of the 1st Order
Lychagin, Valentin V. (Working paper; Arbeidsnotat, 20081209)The problem of local feedback equivalence for 1dimensional control systems of the 1st order is considered. The algebra of differential invariants and criteria for the feedback equivalence for regular control systems are ... 
Geodesic Webs and PDE Systems of Euler Equations
Goldberg, Vladislav V.; Lychagin, Valentin V. (Journal article; Tidsskriftartikkel; Peer reviewed, 20081030)We find necessary and sufficient conditions for the foliation defined by level sets of a function f(x1, ..., xn) to be totally geodesic in a torsionfree connection and apply them to find the conditions for dwebs of ... 
Geodesic Webs of Hypersurfaces
Goldberg, Vladislav V.; Lychagin, Valentin V. (Working paper; Arbeidsnotat, 20081211)In the present paper we study geometric structures associated with webs of hypersurfaces. We prove that with any geodesic (n + 2)web on an ndimensional manifold there is naturally associated a unique projective structure ... 
Geodesic Webs on a TwoDimensional Manifold and Euler Equations
Lychagin, Valentin V.; Goldberg, Vladislav V. (Journal article; Tidsskriftartikkel; Peer reviewed, 20081030)We prove that any planar 4web defines a unique projective structure in the plane in such a way that the leaves of the web foliations are geodesics of this projective structure. We also find conditions for the projective ... 
Invariants of pseudogroup actions: Homological methods and Finiteness theorem
Kruglikov, Boris; Lychagin, Valentin V. (Working paper; Arbeidsnotat, 20051207)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 lvariants ... 
Linearizability of dwebs, d ≥ 4, on twodimensional manifolds
Goldberg, Vladislav V.; Lychagin, Valentin V.; Akivis, Maks A. (Journal article; Tidsskriftartikkel; Peer reviewed, 20040331)We find d − 2 relative differential invariants for a dweb, d ≥ 4, on a twodimensional manifold and prove that their vanishing is necessary and sufficient for a dweb to be linearizable. If one writes the above ... 
On a class of linearizable planar geodesic webs
Lychagin, Valentin V.; Goldberg, Vladislav V. (Working paper; Arbeidsnotat, 20081213)We present a complete description of a class of linearizable planar geodesic webs which contain a parallelizable 3subweb. 
On Rank Problems for Planar Webs and Projective Structures
Lychagin, Valentin V.; Goldberg, Vladislav V. (Chapter; Bokkapittel, 20081203)We present some old and recent results on rank problems and linearizability of geodesic planar webs 
On the Blaschke Conjecture for 3Webs
Lychagin, Valentin V.; Goldberg, Vladislav V. (Journal article; Tidsskriftartikkel; Peer reviewed, 20041121)We find relative differential invariants of orders eight and nine for a planar nonparallelizable 3web such that their vanishing is necessary and sufficient for a 3web to be linearizable. This solves the Blaschke conjecture ... 
Spencer δcohomology, restrictions, characteristics and involutive symbolic PDEs
Kruglikov, Boris; Lychagin, Valentin V. (Working paper; Arbeidsnotat, 20050307)We generalize the notion of involutivity to systems of differential equations of different orders and show that the classical results relating involutivity, restrictions, characteristics and characteristicity, known for ... 
Theory of linear Gdifference equations
Lychagin, Valentin V.; Jakobsen, Per K. (Journal article; Tidsskriftartikkel; Peer reviewed, 19971217)We introduce the notion of difference equation defined on a structured set. The symmetry group of the structure determines the set of difference operators. All main notions in the theory of difference equations are introduced ...