2,026 research outputs found
Non-avoided crossings for n-body balanced configurations in R^3 near a central configuration
The balanced configurations are those n-body configurations which admit a
relative equilibrium motion in a Euclidean space E of high enough dimension 2p.
They are characterized by the commutation of two symmetric endomorphisms of the
(n-1)-dimensional Euclidean space of codispositions, the intrinsic inertia
endomorphism B which encodes the shape and the Wintner-Conley endomorphism A
which encodes the forces. In general, p is the dimension d of the
configuration, which is also the rank of B. Lowering to 2(d-1) the dimension of
E occurs when the restriction of A to the (invariant) image of B possesses a
double eigenvalue. It is shown that, while in the space of all dxd-symmetric
endomorphisms, having a double eigenvalue is a condition of codimension 2 (the
avoided crossings of physicists), here it becomes of codimension 1 provided
some condition (H) is satisfied. As the condition is always satisfied for
configurations of the maximal dimension (i.e. if d=n-1), this implies in
particular the existence, in the neighborhood of the regular tetrahedron
configuration of 4 bodies with no three of the masses equal, of exactly 3
families of balanced configurations which admit relative equilibrium motion in
a four dimensional space.Comment: 35 pages, 1 diagram, 6 figures Section 1.5.2 is new: it introduces
the condition (H) which had been overlooked in the first versio
Robust transitivity for endomorphisms admitting critical points
We address the problem of giving necessary and sufficient conditions in order
to have robustly transitive endomorphisms admitting persistent critical sets.
We exhibit different type of open examples of robustly transitive maps in any
isotopic class of endomorphisms acting on the two dimensional torus admitting
persistent critical points. We also provide some necessary condition for robust
transitivity in this setting.Comment: 15 pages, 3 figure
Non-critical equivariant L-values of modular abelian varieties
We prove an equivariant version of Beilinson's conjecture on non-critical
-values of strongly modular abelian varieties over number fields. As an
application, we prove a weak version of Zagier's conjecture on and
Deninger's conjecture on for non-CM strongly modular
-curves.Comment: 18 page
Holomorphic self-maps of singular rational surfaces
We give a new proof of the classification of normal singular surface germs
admitting non-invertible holomorphic self-maps and due to J. Wahl. We then draw
an analogy between the birational classification of singular holomorphic
foliations on surfaces, and the dynamics of holomorphic maps. Following this
analogy, we introduce the notion of minimal holomorphic model for holomorphic
maps. We give sufficient conditions which ensure the uniqueness of such a
model.Comment: 37 pages. To appear in Publicacions Matematiques
Webs invariant by rational maps on surfaces
We prove that under mild hypothesis rational maps on a surface preserving
webs are of Latt\`es type. We classify endomorphisms of P^2 preserving webs,
extending former results of Dabija-Jonsson.Comment: 27 pages, submitte
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