Displaying similar documents to “Local structural stability of C 2 integrable 1-forms”

Poincaré-Hopf index and partial hyperbolicity

C. A Morales (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

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We use the theory of partially hyperbolic systems [HPS] in order to find singularities of index 1 for vector fields with isolated zeroes in a 3 -ball. Indeed, we prove that such zeroes exists provided the maximal invariant set in the ball is partially hyperbolic, with volume expanding central subbundle, and the strong stable manifolds of the singularities are unknotted in the ball.

Smooth linearization of germs of R 2 -actions and holomorphic vector fields

F. Dumortier, Robert Roussarie (1980)

Annales de l'institut Fourier

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The paper contains a generic condition permitting the linearization in class 𝒞 k , 0 ≤ k ≤ ∞ , of germs of singular infinitesimal R 2 -actions on R n ( n ≥ 2 ) and of singular holomorphic vector fields on C n ( n ≥ 1 ) . It generalizes a similar result of S. Sternberg for germs of singular (real) vector fields on R n .

Global stability for diagrams of differentiable applications

Luis Antonio Favaro, C. M. Mendes (1986)

Annales de l'institut Fourier

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In this paper, we give some examples which point to the non-existence of C ∞ -global stable diagrams R ← g M → f R , M compact. If Φ : M → Q is fixed we define the Φ -equivalence for maps f : M → P and the corresponding Φ -stability. The globalization procedure works and we can compare the Φ -stability, Φ -infinitesimal stability, and Φ -homotopical stability. Also we give some characterization theorems for lower dimensions.