6533b82efe1ef96bd1292860
RESEARCH PRODUCT
Some topological invariants for three-dimensional flows
Emmanuel Dufrainesubject
Invariant polynomialApplied MathematicsMathematical analysisInvariant manifoldGeneral Physics and AstronomyStatistical and Nonlinear PhysicsFinite type invariantConjugacy classHeteroclinic orbitHomoclinic orbitInvariant (mathematics)Mathematical PhysicsCenter manifoldMathematicsdescription
We deal here with vector fields on three manifolds. For a system with a homoclinic orbit to a saddle-focus point, we show that the imaginary part of the complex eigenvalues is a conjugacy invariant. We show also that the ratio of the real part of the complex eigenvalue over the real one is invariant under topological equivalence. For a system with two saddle-focus points and an orbit connecting the one-dimensional invariant manifold of those points, we compute a conjugacy invariant related to the eigenvalues of the vector field at the singularities. (c) 2001 American Institute of Physics.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2001-09-01 | Chaos: An Interdisciplinary Journal of Nonlinear Science |