Displaying similar documents to “Smooth normalization of a vector field near a semistable limit cycle”

Smoothness property for bifurcation diagrams.

Robert Roussarie (1997)

Publicacions Matemàtiques

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Strata of bifurcation sets related to the nature of the singular points or to connections between hyperbolic saddles in smooth families of planar vector fields, are smoothly equivalent to subanalytic sets. But it is no longer true when the bifurcation is related to transition near singular points, for instance for a line of double limit cycles in a generic 2-parameter family at its end point which is a codimension 2 saddle connection bifurcation point. This line has a flat contact with...

The modified diagonal cycle on the triple product of a pointed curve

Benedict H. Gross, Chad Schoen (1995)

Annales de l'institut Fourier

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Let X be a curve over a field k with a rational point e . We define a canonical cycle Δ e ∈ Z 2 ( X 3 ) hom . Suppose that k is a number field and that X has semi-stable reduction over the integers of k with fiber components non-singular. We construct a regular model of X 3 and show that the height pairing ⟨ τ * ( Δ e ) , τ * ' ( Δ e ) ⟩ is well defined where τ and τ ' are correspondences. The paper ends with a brief discussion of heights and L -functions in the case that X is a modular curve.

Around rationality of cycles

Raphaël Fino (2013)

Open Mathematics

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We prove certain results comparing rationality of algebraic cycles over the function field of a quadric and over the base field. These results have already been obtained by Alexander Vishik in the case of characteristic 0, which allowed him to work with algebraic cobordism theory. Our proofs use the modulo 2 Steenrod operations in the Chow theory and work in any characteristic ≠ 2.

The explosion of singular cycles

Rodrigo Bamon, Rafael Labarca, Ricardo Mañé, Maria-José Pacífico (1993)

Publications Mathématiques de l'IHÉS

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