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On integrability of certain rank 2 sub-Riemannian structures

Result description

We discuss rank 2 sub-Riemannian structures on low-dimensional manifolds and prove that some of these structures in dimensions 6, 7 and 8 have a maximal amount of symmetry but no integrals polynomial in momenta of low degrees, except for those coming from the Killing vector fields and the Hamiltonian, thus indicating nonintegrability of the corresponding geodesic flows.

Keywords

sub-Riemannian geodesic flowKilling tensorintegral

The result's identifiers

Alternative languages

  • Result language

    angličtina

  • Original language name

    On integrability of certain rank 2 sub-Riemannian structures

  • Original language description

    We discuss rank 2 sub-Riemannian structures on low-dimensional manifolds and prove that some of these structures in dimensions 6, 7 and 8 have a maximal amount of symmetry but no integrals polynomial in momenta of low degrees, except for those coming from the Killing vector fields and the Hamiltonian, thus indicating nonintegrability of the corresponding geodesic flows.

  • Czech name

    —

  • Czech description

    —

Classification

  • Type

    Jimp - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

    —

  • OECD FORD branch

    10308 - Astronomy (including astrophysics,space science)

Result continuities

Others

  • Publication year

    2017

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Regular & Chaotic Dynamics

  • ISSN

    1560-3547

  • e-ISSN

    —

  • Volume of the periodical

    22

  • Issue of the periodical within the volume

    5

  • Country of publishing house

    RU - RUSSIAN FEDERATION

  • Number of pages

    18

  • Pages from-to

    502-519

  • UT code for WoS article

    000412030900003

  • EID of the result in the Scopus database

    2-s2.0-85030173416

Result type

Jimp - Article in a specialist periodical, which is included in the Web of Science database

Jimp

OECD FORD

Astronomy (including astrophysics,space science)

Year of implementation

2017

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