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Reduction of cluster iteration maps
Discriminantly separable polynomials and quad-equations
1. | The Department of Mathematical Sciences, University of Texas at Dallas, 800 West Campbell Road, Richardson TX 75080, United States |
2. | Faculty for Traffic and Transport Engineering, University of Belgrade, Vojvode Stepe 305, 11000 Belgrade, Serbia |
References:
[1] |
V. E. Adler, A. I. Bobenko and Y. B. Suris, Classification of integrable equations on quad-graphs. The consistency approach,, Commun. Math. Phys., 233 (2003), 513.
|
[2] |
V. E. Adler, A. I. Bobenko and Y. B. Suris, Discrete nonlinear hiperbolic equations. Classification of integrable cases,, Funct. Anal. Appl, 43 (2009), 3.
doi: 10.1007/s10688-009-0002-5. |
[3] |
V. E. Adler, A. I. Bobenko and Yu. B. Suris, Geometry of Yang-Baxter maps: Pencils of conics and quadrirational mappings,, Comm. Anal. Geom., 12 (2004), 967.
doi: 10.4310/CAG.2004.v12.n5.a1. |
[4] |
A. I. Bobenko and Yu. B. Suris, Integrable noncommutative equations on quad-graphs. The consistency approach,, Lett. Math. Phys., 61 (2002), 241.
doi: 10.1023/A:1021249131979. |
[5] |
A. I. Bobenko and Yu. B. Suris, Integrable systems on quad-graphs,, Int. Math. Res. Not., (2002), 573.
doi: 10.1155/S1073792802110075. |
[6] |
V. Buchstaber, n-valued groups: Theory and applications,, Moscow Mathematical Journal, 6 (2006), 57.
|
[7] |
V. M. Buchstaber, Functional equations, associated with addition theorems for elliptic functions, and two-valued algebraic groups,, Russian Math. Surv., 45 (1990), 213.
doi: 10.1070/RM1990v045n03ABEH002361. |
[8] |
V. M. Buchstaber and V. Dragović, Two-valued groups, Kummer varieties and integrable billiards,, preprint, (). Google Scholar |
[9] |
V. M. Buchstaber and S. P. Novikov, Formal groups, power systems and Adams operators,, Mat. Sb. (N. S), 84(126) (1971), 81.
|
[10] |
V. M. Buchstaber and A. P. Veselov, Integrable correspondences and algebraic representations of multivalued groups,, Internat. Math. Res. Notices, 8 (1996), 381.
doi: 10.1155/S1073792896000256. |
[11] |
G. Darboux, Principes de Géométrie Analytique,, Gauthier-Villars, (1917). Google Scholar |
[12] |
V. Dragović, Poncelet-Darboux curves, their complete decomposition and Marden theorem,, Int. Math. Res. Notes, 2011 (2011), 3502.
doi: 10.1093/imrn/rnq229. |
[13] |
V. Dragović, Generalization and geometrization of the Kowalevski top,, Communications in Math. Phys., 298 (2010), 37.
doi: 10.1007/s00220-010-1066-z. |
[14] |
V. Dragović and K. Kukić, New examples of systems of the Kowalevski type,, Regular and Chaotic Dynamics, 16 (2011), 484.
doi: 10.1134/S1560354711050054. |
[15] |
V. Dragović and K. Kukić, Systems of the Kowalevski type and discriminantly separable polynomials,, Regular and Chaotic Dynamics, 19 (2014), 162.
doi: 10.1134/S1560354714020026. |
[16] |
V. Dragović and M. Radnović, Poncelet Porisms and Beyond,, Springer, (2011).
doi: 10.1007/978-3-0348-0015-0. |
[17] |
V. Dragović and M. Radnović, Billiard algebra, integrable line congruences and DR-nets,, J. Nonlinear Mathematical Physics, 19 (2012).
doi: 10.1142/S1402925112500192. |
[18] |
V. V. Golubev, Lectures on the Integration of Motion of a Heavy Rigid Body Around a Fixed Point,, Gostechizdat, (1953).
|
[19] |
S. Kowalevski, Sur la probleme de la rotation d'un corps solide autour d'un point fixe,, Acta Math., 12 (1889), 177.
doi: 10.1007/BF02592182. |
[20] |
J. G. Semple and G. T. Kneebone, Algebraic Projective Geometry,, Clarendon Press, (1998).
|
show all references
References:
[1] |
V. E. Adler, A. I. Bobenko and Y. B. Suris, Classification of integrable equations on quad-graphs. The consistency approach,, Commun. Math. Phys., 233 (2003), 513.
|
[2] |
V. E. Adler, A. I. Bobenko and Y. B. Suris, Discrete nonlinear hiperbolic equations. Classification of integrable cases,, Funct. Anal. Appl, 43 (2009), 3.
doi: 10.1007/s10688-009-0002-5. |
[3] |
V. E. Adler, A. I. Bobenko and Yu. B. Suris, Geometry of Yang-Baxter maps: Pencils of conics and quadrirational mappings,, Comm. Anal. Geom., 12 (2004), 967.
doi: 10.4310/CAG.2004.v12.n5.a1. |
[4] |
A. I. Bobenko and Yu. B. Suris, Integrable noncommutative equations on quad-graphs. The consistency approach,, Lett. Math. Phys., 61 (2002), 241.
doi: 10.1023/A:1021249131979. |
[5] |
A. I. Bobenko and Yu. B. Suris, Integrable systems on quad-graphs,, Int. Math. Res. Not., (2002), 573.
doi: 10.1155/S1073792802110075. |
[6] |
V. Buchstaber, n-valued groups: Theory and applications,, Moscow Mathematical Journal, 6 (2006), 57.
|
[7] |
V. M. Buchstaber, Functional equations, associated with addition theorems for elliptic functions, and two-valued algebraic groups,, Russian Math. Surv., 45 (1990), 213.
doi: 10.1070/RM1990v045n03ABEH002361. |
[8] |
V. M. Buchstaber and V. Dragović, Two-valued groups, Kummer varieties and integrable billiards,, preprint, (). Google Scholar |
[9] |
V. M. Buchstaber and S. P. Novikov, Formal groups, power systems and Adams operators,, Mat. Sb. (N. S), 84(126) (1971), 81.
|
[10] |
V. M. Buchstaber and A. P. Veselov, Integrable correspondences and algebraic representations of multivalued groups,, Internat. Math. Res. Notices, 8 (1996), 381.
doi: 10.1155/S1073792896000256. |
[11] |
G. Darboux, Principes de Géométrie Analytique,, Gauthier-Villars, (1917). Google Scholar |
[12] |
V. Dragović, Poncelet-Darboux curves, their complete decomposition and Marden theorem,, Int. Math. Res. Notes, 2011 (2011), 3502.
doi: 10.1093/imrn/rnq229. |
[13] |
V. Dragović, Generalization and geometrization of the Kowalevski top,, Communications in Math. Phys., 298 (2010), 37.
doi: 10.1007/s00220-010-1066-z. |
[14] |
V. Dragović and K. Kukić, New examples of systems of the Kowalevski type,, Regular and Chaotic Dynamics, 16 (2011), 484.
doi: 10.1134/S1560354711050054. |
[15] |
V. Dragović and K. Kukić, Systems of the Kowalevski type and discriminantly separable polynomials,, Regular and Chaotic Dynamics, 19 (2014), 162.
doi: 10.1134/S1560354714020026. |
[16] |
V. Dragović and M. Radnović, Poncelet Porisms and Beyond,, Springer, (2011).
doi: 10.1007/978-3-0348-0015-0. |
[17] |
V. Dragović and M. Radnović, Billiard algebra, integrable line congruences and DR-nets,, J. Nonlinear Mathematical Physics, 19 (2012).
doi: 10.1142/S1402925112500192. |
[18] |
V. V. Golubev, Lectures on the Integration of Motion of a Heavy Rigid Body Around a Fixed Point,, Gostechizdat, (1953).
|
[19] |
S. Kowalevski, Sur la probleme de la rotation d'un corps solide autour d'un point fixe,, Acta Math., 12 (1889), 177.
doi: 10.1007/BF02592182. |
[20] |
J. G. Semple and G. T. Kneebone, Algebraic Projective Geometry,, Clarendon Press, (1998).
|
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