Displaying similar documents to “Faà di Bruno's formula and nonhyperbolic fixed points of one-dimensional maps.”

A Note on the Uniqueness of Stable Marriage Matching

Ewa Drgas-Burchardt (2013)

Discussiones Mathematicae Graph Theory

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In this note we present some sufficient conditions for the uniqueness of a stable matching in the Gale-Shapley marriage classical model of even size. We also state the result on the existence of exactly two stable matchings in the marriage problem of odd size with the same conditions.

Around stable forking

Byunghan Kim, A. Pillay (2001)

Fundamenta Mathematicae

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We discuss various conjectures and problems around the issue of when and whether stable formulas are responsible for forking in simple theories. We prove that if the simple theory T has strong stable forking then any complete type is a nonforking extension of a complete type which is axiomatized by instances of stable formulas. We also give another treatment of the first author's result which identifies canonical bases in supersimple theories.

C¹ stable maps: examples without saddles

J. Iglesias, A. Portela, A. Rovella (2010)

Fundamenta Mathematicae

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We give here the first examples of C¹ structurally stable maps on manifolds of dimension greater than two that are neither diffeomorphisms nor expanding. It is shown that an Axiom A endomorphism all of whose basic pieces are expanding or attracting is C¹ stable. A necessary condition for the existence of such examples is also given.

Second-order sufficient condition for ℓ ˜ -stable functions

Dušan Bednařík, Karel Pastor (2007)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The aim of our article is to present a proof of the existence of local minimizer in the classical optimality problem without constraints under weaker assumptions in comparisons with common statements of the result. In addition we will provide rather elementary and self-contained proof of that result.

Compositions of equi-dimensional fold maps

Yoshihiro Hirato, Masamichi Takase (2012)

Fundamenta Mathematicae

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According to Ando's theorem, the oriented bordism group of fold maps of n-manifolds into n-space is isomorphic to the stable n-stem. Among such fold maps we define two geometric operations corresponding to the composition and to the Toda bracket in the stable stem through Ando's isomorphism. By using these operations we explicitly construct several fold maps with convenient properties, including a fold map which represents the generator of the stable 6-stem.

Ω-stability for maps with nonwandering critical points

J. Delgado, N. Romero, A. Rovella, F. Vilamajó (2007)

Fundamenta Mathematicae

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Sufficient conditions for a map having nonwandering critical points to be Ω-stable are introduced. It is not known if these conditions are necessary, but they are easily verified for all known examples of Ω-stable maps. Their necessity is shown in dimension two. Examples are given of Axiom A maps that have no cycles but are not Ω-stable.