Geodesic
Elliptical Billiards in the Minkowski Plane and Extremal Polynomials
Russian journal of nonlinear dynamics, Tome 15 (2019) no. 4, pp. 397-407

Voir la notice de l'article provenant de la source Math-Net.Ru

We derive necessary and sufficient conditions for periodic trajectories of billiards within an ellipse in the Minkowski plane in terms of an underlying elliptic curve. Equivalent conditions are derived in terms of polynomial-functional equations as well. The corresponding polynomials are related to the classical extremal polynomials. Similarities and differences with respect to the previously studied Euclidean case are indicated.
Keywords: Minkowski plane, elliptical billiards, elliptic curve, Akhiezer polynomials. 
@article{ND_2019_15_4_a1,
     author = {A. K. Adabrah and V. Dragovi\'c and M. Radnovi\'c},
     title = {Elliptical {Billiards} in the {Minkowski} {Plane} and {Extremal} {Polynomials}},
     journal = {Russian journal of nonlinear dynamics},
     pages = {397--407},
     publisher = {mathdoc},
     volume = {15},
     number = {4},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ND_2019_15_4_a1/}
}
TY  - JOUR
AU  - A. K. Adabrah
AU  - V. Dragović
AU  - M. Radnović
TI  - Elliptical Billiards in the Minkowski Plane and Extremal Polynomials
JO  - Russian journal of nonlinear dynamics
PY  - 2019
SP  - 397
EP  - 407
VL  - 15
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2019_15_4_a1/
LA  - en
ID  - ND_2019_15_4_a1
ER  - 
%0 Journal Article
%A A. K. Adabrah
%A V. Dragović
%A M. Radnović
%T Elliptical Billiards in the Minkowski Plane and Extremal Polynomials
%J Russian journal of nonlinear dynamics
%D 2019
%P 397-407
%V 15
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2019_15_4_a1/
%G en
%F ND_2019_15_4_a1
A. K. Adabrah; V. Dragović; M. Radnović. Elliptical Billiards in the Minkowski Plane and Extremal Polynomials. Russian journal of nonlinear dynamics, Tome 15 (2019) no. 4, pp. 397-407. http://geodesic.mathdoc.fr/item/ND_2019_15_4_a1/