Institutt for matematikk og statistikk: Recent submissions

Now showing items 341-360 of 389

    • Strictly non-proportional geodesically equivalent metrics have htop(g) = 0 

      Matveev, Vladimir S.; Kruglikov, Boris (Journal article; Tidsskriftartikkel; Peer reviewed, 2004-10-24)
      If a closed manifold M possesses two Riemannian metrics which have the same unparameterized geodesics and are not strictly proportional at each point, then the topological entropy of both geodesic flows is zero. This is the main result of the paper and it has many dynamical and topological corollaries. In particular, such a manifoldM should be finitely covered by the product of a rationally ...

    • Invariants and submanifolds in almost complex geometry 

      Kruglikov, Boris (Chapter; Bokkapittel, 2007-12-20)
      In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of higher-dimensional pseudoholomorphic submanifolds.

    • The Kobayashi pseudodistance on almost complex manifolds 

      Overholt, Marius; Kruglikov, Boris S. (Working paper; Arbeidsnotat, 1997-03-06)
      We extend the definition of the Kobayashi pseudodistance to almost complex manifolds and show that its familiar properties are for the most part preserved. We also study the automorphism group of an almost complex manifold and finish with some examples.

    • Anomaly of linearization and auxiliary integrals 

      Kruglikov, Boris (Chapter; Bokkapittel, 2007-12-20)
      In this note we discuss some formal properties of universal linearization operator, relate this to brackets of non-linear differential operators and discuss application to the calculus of auxiliary integrals, used in compatibility reductions of PDEs.

    • Examples of integrable sub-Riemannian geodesic flows 

      Kruglikov, Boris (Journal article; Tidsskriftartikkel; Peer reviewed, 2001-10-22)
      We exhibit examples of sub-Riemannian metrics with integrable geodesic flows and positive topological entropy.

    • Existence of close pseudoholomorphic disks for almost complex manifolds and an applications to Kobayashi-Royden pseudonorm 

      Kruglikov, Boris (Journal article; Tidsskriftartikkel; Peer reviewed, 2000-02-23)
      It is proved in the paper that near every pseudoholomorphic disk on an almost complex manifold a disk of almost the same size in any close direction passes. As an application the Kobayashi-Royden pseudonorm for almost complex manifolds is defined and studied.

    • Tangent and normal bundles in almost complex geometry 

      Kruglikov, Boris (Journal article; Tidsskriftartikkel; Peer reviewed, 2005-06-10)
      We define and study pseudoholomorphic vector bundles structures, particular cases of which are tangent and normal bundle almost complex structures. As an application we deduce normal forms of 1-jets of almost complex structures along a pseudoholomorphic submanifold. In dimension four we relate these normal forms to the problem of pseudoholomorphic foliation of a neighborhood of a curve and the ...

    • Invariant characterization of Liouville metrics and polynomial integrals 

      Kruglikov, Boris (Journal article; Tidsskriftartikkel; Peer reviewed, 2007-09-04)
      A criterion in terms of differential invariants for a metric on a surface to be Liouville is established. Moreover, in this paper we completely solve in invariant terms the local mobility problem of a 2D metric, considered by Darboux: How many quadratic in momenta integrals does the geodesic flow of a given metric possess? The method is also applied to recognition of other polynomial integrals ...

    • Deformation of big pseudoholomorphic disks and application to the Hanh pseudonorm 

      Kruglikov, Boris (Journal article; Tidsskriftartikkel; Peer reviewed, 2003-04-14)
      We simplify proof of the theorem that close to any pseudoholomorphic disk there passes a pseudoholomorphic disk of arbitrary close size with any pre-described sufficiently close direction. We apply these results to the Kobayashi and Hanh pseudodistances. It is shown they coincide in dimensions higher than four. The result is new even in the complex case.

    • Point classification of 2nd order ODEs: Tresse classification revisited and beyond 

      Kruglikov, Boris (Chapter; Bokkapittel, 2008-09-26)
      In 1896 Tresse gave a complete description of relative differential invariants for the pseudogroup action of point transformations on the 2nd order ODEs. The purpose of this paper is to review, in light of modern geometric approach to PDEs, this classification and also discuss the role of absolute invariants and the equivalence problem.

    • Involutivity of field equations 

      Kruglikov, Boris (Working paper; Arbeidsnotat, 2009-02-10)
      We prove involutivity of Einstein and Einstein-Maxwell equations by calculating the Spencer cohomology of these systems. Relation with Cartan method is traced in details. Basic implications through Cartan-Kähler theory are derived.

    • Applying the ICM algorithm for separating pictures consisting of two main parts, background and object application to fMRI recordings and mole pictures 

      Larsen, Are (Master thesis; Mastergradsoppgave, 2009-05-15)
      This work concentrates on using the ICM algorithm for image restoration. The algorithm has been applied to fMRI recordings and mole pictures

    • Distributing a private key generator in Ad hoc Networks 

      Stenberg, Eystein Måløy (Master thesis; Mastergradsoppgave, 2009-05-15)
      A Mobile Ad hoc Network (MANET) is a wireless network that does not rely on a fixed infrastructure. These characteristics make algorithms that route network traffic particularly vulnerable to attack. Mechanisms used to protect against such attacks often depend on cryptographic keys. Since the nodes in a MANET have limited resources, designing methods for cryptographic key management is ...

    • 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 as invariants of the action of the symmetry group. Linear equations are modules over the skew group algebra, solutions are morphisms relating a given equation to other ...

    • 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 are shown to be symmetric monoidal categories in their own right and are found to be isomorphic to certain categories of A−A bicomodules. Properties of relations are ...

    • 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 invariants in terms of web functions f(x, y) and g4(x, y), ..., gd(x, y), then necessary and sufficient conditions for the linearizabilty of a d-web are two PDEs of the fourth order ...

    • On the Blaschke Conjecture for 3-Webs 

      Goldberg, Vladislav V.; Lychagin, Valentin 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 for 3-webs. As a side result, we show that the number of linearizations in the Gronwall conjecture does not exceed fifteen and give criteria for rigidity of 3-webs.

    • 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 and l-covariants, even in the case of non-integrable pseudogroup. Their calculation is based on the cohomological machinery: We introduce a complex for covariants, define their cohomology ...

    • 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 first order systems, extend to the general context. This involves, in particular, a new definition of strong characteristicity. The proof exploits a spectral sequence relating ...

    • 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 in details the case of the motion group O(n) ⋉ R<sup>n</sup> acting on the full (unconstraint) jet-space as well as on some invariant equations.