On the number of connected components in the space of M-polynomials in hyperbolic functions

Boris Shapiro; Alek Vainshtein

doi:10.1016/S0196-8858(02)00536-5

On the number of connected components in the space of M-polynomials in hyperbolic functions

Research output: Contribution to journal › Review article › peer-review

Abstract

We calculate the number of connected components in the space of the so-called M-polynomials of a given degree in hyperbolic functions. By definition an M-polynomial is characterized by the condition that all its critical values are real and distinct.

Original language	English
Pages (from-to)	273-282
Number of pages	10
Journal	Advances in Applied Mathematics
Volume	30
Issue number	1-2
DOIs	https://doi.org/10.1016/S0196-8858(02)00536-5
State	Published - 2003

Bibliographical note

Funding Information:
The authors are sincerely grateful to the Max-Planck Institut für Mathematik in Bonn for the financial support and the excellent research atmosphere during their work on this project in the fall of 2000. Sincere thanks goes to M. Shapiro for the number of important observations which improved essentially some formulations and the general exposition, and especially to A. Eremenko who suggested a similar project during the fall of 1999.

ASJC Scopus subject areas

Applied Mathematics

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10.1016/S0196-8858(02)00536-5

Cite this

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title = "On the number of connected components in the space of M-polynomials in hyperbolic functions",

abstract = "We calculate the number of connected components in the space of the so-called M-polynomials of a given degree in hyperbolic functions. By definition an M-polynomial is characterized by the condition that all its critical values are real and distinct.",

author = "Boris Shapiro and Alek Vainshtein",

note = "Funding Information: The authors are sincerely grateful to the Max-Planck Institut f{\"u}r Mathematik in Bonn for the financial support and the excellent research atmosphere during their work on this project in the fall of 2000. Sincere thanks goes to M. Shapiro for the number of important observations which improved essentially some formulations and the general exposition, and especially to A. Eremenko who suggested a similar project during the fall of 1999.",

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AU - Vainshtein, Alek

N1 - Funding Information: The authors are sincerely grateful to the Max-Planck Institut für Mathematik in Bonn for the financial support and the excellent research atmosphere during their work on this project in the fall of 2000. Sincere thanks goes to M. Shapiro for the number of important observations which improved essentially some formulations and the general exposition, and especially to A. Eremenko who suggested a similar project during the fall of 1999.

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N2 - We calculate the number of connected components in the space of the so-called M-polynomials of a given degree in hyperbolic functions. By definition an M-polynomial is characterized by the condition that all its critical values are real and distinct.

AB - We calculate the number of connected components in the space of the so-called M-polynomials of a given degree in hyperbolic functions. By definition an M-polynomial is characterized by the condition that all its critical values are real and distinct.

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DO - 10.1016/S0196-8858(02)00536-5

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JO - Advances in Applied Mathematics

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On the number of connected components in the space of M-polynomials in hyperbolic functions

Abstract

Bibliographical note

ASJC Scopus subject areas

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