ON THE STRUCTURE OF THE RESONANCE SET OF A REAL POLYNOMIAL
https://doi.org/10.22405/2226-8383-2016-17-3-5-17
Abstract
We consider the resonance set of a real polynomial, i.e. the set of all the points of the coefficient space at which the polynomial has commensurable roots. The resonance set of a polynomial can be considered as a certain generalization of its discriminant set. The structure of the resonance set is useful for investigation of resonances near stationary point of a dynamical system.
The constructive algorithm of computation of polynomial parametrization of the resonance set is provided. The structure of the resonance set of a polynomial of degree \(n\) is described in terms of partitions of the number \(n\).
The main algorithms, described in the paper, are organized as a library of the computer algebra system \(Maple\). The description of the resonance set of a cubic polynomial is given.
About the Author
A. B. Batkhin
Keldysh Institute of Applied Mathematics RAS
Russian Federation
Russian Federation
candidate of fisical and mathematical sciences, associate professor, senior researcher,
Moscow
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Review
For citations:
Batkhin A.B. ON THE STRUCTURE OF THE RESONANCE SET OF A REAL POLYNOMIAL. Chebyshevskii Sbornik. 2016;17(3):5-17. (In Russ.) https://doi.org/10.22405/2226-8383-2016-17-3-5-17
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