5,634 research outputs found
Asymmetric function theory
The classical theory of symmetric functions has a central position in
algebraic combinatorics, bridging aspects of representation theory,
combinatorics, and enumerative geometry. More recently, this theory has been
fruitfully extended to the larger ring of quasisymmetric functions, with
corresponding applications. Here, we survey recent work extending this theory
further to general asymmetric polynomials.Comment: 36 pages, 8 figures, 1 table. Written for the proceedings of the
Schubert calculus conference in Guangzhou, Nov. 201
The boundary of hyperbolicity for Henon-like families
We consider C^{2} Henon-like families of diffeomorphisms of R^{2} and study
the boundary of the region of parameter values for which the nonwandering set
is uniformly hyperbolic. Assuming sufficient dissipativity, we show that the
loss of hyperbolicity is caused by a first homoclinic or heteroclinic tangency
and that uniform hyperbolicity estimates hold uniformly in the parameter up to
this bifurcation parameter and even, to some extent, at the bifurcation
parameter.Comment: 32 pages, 11 figures. Several minor revisions, additional figures,
clarifications of some argument
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