A Chebyshev criterion for Abelian integrals

By Maite Grau, Francesc Mañosas, Jordi Villadelprat. 2008

155 citations recorded by the source corpus.

We present a criterion that provides an easy sufficient condition in order for a collection of Abelian integrals to have the Chebyshev property. This condition involves the functions in the integrand of the Abelian integrals and can be checked, in many cases, in a purely algebraic way. By using this criterion, several known results are obtained in a shorter way and some new results, which could not be tackled by the known standard methods, can also be deduced.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/44a44e7f89f6cc4b20fb4739cc9ff0bc82eefc69

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In Applied Mathematics

1. Jordi Villadelprat
2. Francesc Mañosas
3. Maite Grau

In Geometry and Topology

1. Jordi Villadelprat
2. Maite Grau
3. Francesc Mañosas

Citations in the corpus

• Bounding the number of zeros of certain Abelian integrals (2011, methodology): “Grau [12] we provided a sufficient condition in order for a collection of Abelian integrals I0(h), I1(h), .”
• Bifurcation of critical periods from Pleshkan's isochrones (2008, methodology): “) We note that analogous computations to the ones carried out in the previous section and the application of the criterion given in [12] also yield the proof of Lemma 4.”