Now showing items 1-17 of 17

  • Abelian equations and rank problems for planar webs 

    Lychagin, Valentin V.; Goldberg, Vladislav V. (Journal article; Tidsskriftartikkel; Peer reviewed, 2006-05-04)
    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 ...
  • The categorical theory of relations and quantization 

    Lychagin, Valentin V.; Jakobsen, Per K. (Working paper; Arbeidsnotat, 2001-10-30)
    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, multi-brackets and integrability of systems of PDEs 

    Kruglikov, Boris; Lychagin, Valentin V. (Journal article; Tidsskriftartikkel; Peer reviewed, 2008-02-20)
    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 ...
  • Differential invariants of the motion group actions 

    Kruglikov, Boris; Lychagin, Valentin V. (Working paper; Arbeidsnotat, 2007-12-20)
    Differential invariants of a (pseudo)group action can vary when restricted to invariant submanifolds (differential equations). The algebra is still governed by the Lie-Tresse theorem, but may change a lot. We describe ...
  • Dimension of the solutions space of PDEs 

    Kruglikov, Boris; Lychagin, Valentin V. (Conference object; Konferansebidrag, 2006-10-26)
    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, 2008-12-07)
    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 1-dimensional Control Systems of the 1-st Order 

    Lychagin, Valentin V. (Working paper; Arbeidsnotat, 2008-12-09)
    The problem of local feedback equivalence for 1-dimensional control systems of the 1-st 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, 2008-10-30)
    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 torsion-free connection and apply them to find the conditions for d-webs of ...
  • Geodesic Webs of Hypersurfaces 

    Goldberg, Vladislav V.; Lychagin, Valentin V. (Working paper; Arbeidsnotat, 2008-12-11)
    In the present paper we study geometric structures associated with webs of hypersurfaces. We prove that with any geodesic (n + 2)-web on an n-dimensional manifold there is naturally associated a unique projective structure ...
  • Geodesic Webs on a Two-Dimensional Manifold and Euler Equations 

    Lychagin, Valentin V.; Goldberg, Vladislav V. (Journal article; Tidsskriftartikkel; Peer reviewed, 2008-10-30)
    We prove that any planar 4-web 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, 2005-12-07)
    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 ...
  • Linearizability of d-webs, d ≥ 4, on two-dimensional manifolds 

    Goldberg, Vladislav V.; Lychagin, Valentin V.; Akivis, Maks A. (Journal article; Tidsskriftartikkel; Peer reviewed, 2004-03-31)
    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 ...
  • On a class of linearizable planar geodesic webs 

    Lychagin, Valentin V.; Goldberg, Vladislav V. (Working paper; Arbeidsnotat, 2008-12-13)
    We present a complete description of a class of linearizable planar geodesic webs which contain a parallelizable 3-subweb.
  • On Rank Problems for Planar Webs and Projective Structures 

    Lychagin, Valentin V.; Goldberg, Vladislav V. (Chapter; Bokkapittel, 2008-12-03)
    We present some old and recent results on rank problems and linearizability of geodesic planar webs
  • On the Blaschke Conjecture for 3-Webs 

    Lychagin, Valentin V.; Goldberg, Vladislav V. (Journal article; Tidsskriftartikkel; Peer reviewed, 2004-11-21)
    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 ...
  • Spencer δ-cohomology, restrictions, characteristics and involutive symbolic PDEs 

    Kruglikov, Boris; Lychagin, Valentin V. (Working paper; Arbeidsnotat, 2005-03-07)
    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 G-difference equations 

    Lychagin, Valentin V.; Jakobsen, Per K. (Journal article; Tidsskriftartikkel; Peer reviewed, 1997-12-17)
    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 ...