A survey on polynomial in momenta integrals for billiard problems

Standard

A survey on polynomial in momenta integrals for billiard problems. / Bialy, Misha; Mironov, Andrey E.

In: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 376, No. 2131, 20170418, 17.09.2018.

Research output: Contribution to journal › Article › peer-review

Harvard

Bialy, M & Mironov, AE 2018, 'A survey on polynomial in momenta integrals for billiard problems', Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 376, no. 2131, 20170418. https://doi.org/10.1098/rsta.2017.0418

APA

Bialy, M., & Mironov, A. E. (2018). A survey on polynomial in momenta integrals for billiard problems. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 376(2131), [20170418]. https://doi.org/10.1098/rsta.2017.0418

Vancouver

Bialy M, Mironov AE. A survey on polynomial in momenta integrals for billiard problems. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2018 Sept 17;376(2131):20170418. doi: 10.1098/rsta.2017.0418

Author

Bialy, Misha ; Mironov, Andrey E. / A survey on polynomial in momenta integrals for billiard problems. In: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2018 ; Vol. 376, No. 2131.

BibTeX

@article{8367358664b44df9a9e339f3919e9d38,

title = "A survey on polynomial in momenta integrals for billiard problems",

abstract = "In this paper, we give a short survey of recent results on the algebraic version of the Birkhoff conjecture for integrable billiards on surfaces of constant curvature. We also discuss integrable magnetic billiards. As a new application of the algebraic technique, we study the existence of polynomial integrals for the twosided magnetic billiards introduced by Kozlov and Polikarpov. This article is part of the theme issue 'Finite dimensional integrable systems: new trends and methods'.",

keywords = "Birkhoff conjecture, Magnetic billiards, Polynomial integrals, Two-sided magnetic billiards, FIELDS, polynomial integrals, CONVEX BILLIARDS, MAGNETIC BILLIARDS, CLASSICAL BILLIARDS, BIRKHOFF CONJECTURE, CONSTANT CURVATURE, magnetic billiards, two-sided magnetic billiards, SURFACES",

author = "Misha Bialy and Mironov, {Andrey E.}",

year = "2018",

month = sep,

day = "17",

doi = "10.1098/rsta.2017.0418",

language = "English",

volume = "376",

journal = "Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences",

issn = "0962-8428",

publisher = "The Royal Society",

number = "2131",

}

RIS

TY - JOUR

T1 - A survey on polynomial in momenta integrals for billiard problems

AU - Bialy, Misha

AU - Mironov, Andrey E.

PY - 2018/9/17

Y1 - 2018/9/17

N2 - In this paper, we give a short survey of recent results on the algebraic version of the Birkhoff conjecture for integrable billiards on surfaces of constant curvature. We also discuss integrable magnetic billiards. As a new application of the algebraic technique, we study the existence of polynomial integrals for the twosided magnetic billiards introduced by Kozlov and Polikarpov. This article is part of the theme issue 'Finite dimensional integrable systems: new trends and methods'.

AB - In this paper, we give a short survey of recent results on the algebraic version of the Birkhoff conjecture for integrable billiards on surfaces of constant curvature. We also discuss integrable magnetic billiards. As a new application of the algebraic technique, we study the existence of polynomial integrals for the twosided magnetic billiards introduced by Kozlov and Polikarpov. This article is part of the theme issue 'Finite dimensional integrable systems: new trends and methods'.

KW - Birkhoff conjecture

KW - Magnetic billiards

KW - Polynomial integrals

KW - Two-sided magnetic billiards

KW - FIELDS

KW - polynomial integrals

KW - CONVEX BILLIARDS

KW - MAGNETIC BILLIARDS

KW - CLASSICAL BILLIARDS

KW - BIRKHOFF CONJECTURE

KW - CONSTANT CURVATURE

KW - magnetic billiards

KW - two-sided magnetic billiards

KW - SURFACES

UR - http://www.scopus.com/inward/record.url?scp=85054130053&partnerID=8YFLogxK

U2 - 10.1098/rsta.2017.0418

DO - 10.1098/rsta.2017.0418

M3 - Article

C2 - 30224422

AN - SCOPUS:85054130053

VL - 376

JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0962-8428

IS - 2131

M1 - 20170418

ER -

ID: 16947932