Browsing by Author "Fedorov, Yuri"

Algebraic description of jacobians isogeneous to certain prym varieties with polarization (1,2)
Enolski, Viktor Z.; Fedorov, Yuri (20180101)
Article
Open AccessFor a class of nonhyperelliptic genus 3 curves C which are twofold coverings of elliptic curves E, we give an explicit algebraic description of all birationally nonequivalent genus 2 curves whose Jacobians are degree 2 ... 
Algebraic description of Jacobians isogeneous to certain Prym varieties with polarization (1,2)
Fedorov, Yuri; Enolski, Viktor Z. (201411)
External research report
Open AccessFor a class of nonhyperelliptic genus 3 curves C which are 2fold coverings of elliptic curves E, we give an explicit algebraic description of all birationally nonequivalent genus 2 curves whose Jacobians are degree 2 ... 
An ellipsoidal billiard with a quadratic potential
Fedorov, Yuri (2003)
Article
Open AccessThere exists an in infite hierarchy of integrable generalizations of the geodesic flow on an n di mensional ellipsoid.hese generalizations describe the motion of a point in the force fields of certain polynomial potentials.In ... 
AutoBacklund transformations and special integrals for differentialdelay Painlevé hierarchies
Fedorov, Yuri; Ruiz Gordoa, Maria Pilar; Pickering, Andrew (20141001)
Article
Restricted access  publisher's policyThe six Painleve equations have attracted much interest over the last thirty years or so. More recently many authors have begun to explore properties of higherorder versions of both these equations and their discrete ... 
Backlund transformations on coadjoint orbits of the loop algebra gl(n)
Fedorov, Yuri (2003)
Article
Open AccessThere is a wide class of integrable Hamiltonian systems on ﬁnitedimensional coadjoint orbits of the loop algebra ˜ gl(r) which are represented by r × r Lax equations with a rational spectral parameter.A reduced complex ... 
Biasymptotic billiard orbits inside perturbed ellipsoids
Bolotin, S.; Delshams Valdés, Amadeu; Fedorov, Yuri; Ramírez Ros, Rafael (2001)
Article
Open Access 
Closed Geodesics and Billiards on Quadrics related to elliptic KdV solutions
Abenda, Simonetta; Fedorov, Yuri (2004)
Article
Open AccessWe consider algebraic geometrical properties of the integrable billiard on a quadric Q with elastic impacts along another quadric confocal to Q. These properties are in sharp contrast with those of the ellipsoidal Birkho® ... 
Discrete nonholonomic LL systems on Lie groups
Fedorov, Yuri; Zenkov, Dmitry (2003)
Article
Open AccessThis paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic leftinvariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two ... 
Geodesic flows and Neumann systems on Stiefel varieties: geometry and integrability
Fedorov, Yuri (20101203)
Article
Restricted access  publisher's policyWe study integrable geodesic flows on Stiefel varieties Vn,r = SO(n)/SO(n−r ) given by the Euclidean, normal (standard), Manakovtype, and Einstein metrics.We also consider natural generalizations of the Neumann systems ... 
Homoclinic billiard orbits inside symmetrically perturbed ellipsoids
Delshams Valdés, Amadeu; Fedorov, Yuri; Ramírez Ros, Rafael (2000)
Article
Open AccessThe billiard motion inside an ellipsoid of ${\bf R}^{3}$ is completely integrable. If the ellipsoid is not of revolution, there are many orbits biasymptotic to its major axis. The set of biasymptotic orbits is described ... 
Integrable nonholonomic geodesic flows on compact Lie groups
Fedorov, Yuri; Jovanovic, Bozidar D. (2003)
Article
Open AccessThis paper is a review of recent results on integrable nonholonomic geodesic flows of left–invariant metrics and left and right–invariant constraint distributions on compact Lie groups. 
Nonholonomic LR systems as Generalized Chaplygin systems with an invariant measure and geodesic flows on homogeneous spaces
Fedorov, Yuri; Jovanovic, Bozidar D. (2003)
Article
Open AccessWe consider a class of dynamical systems on a compact Lie group G with a leftinvariant metric and rightinvariant nonholonomic constraints (so called LR systems) and show that, under a generic condition on the constraints, ... 
On the construction of elliptic solutions of integrable birational maps
Petrera, Matteo; Pfadler, Andreas; Suris, Yuri B.; Fedorov, Yuri (20170101)
Article
Open AccessWe present a systematic technique to find explicit solutions of birational maps, provided that these solutions are given in terms of elliptic functions. The two main ingredients are the following: (i) application of classical ... 
Separation of variables and explicit thetafunction solution of the classical SteklovLyapunov systems: A geometric and algebraic geometric background
Fedorov, Yuri; Basak Gancheva, Inna (200911)
External research report
Open AccessAbstract The paper revises the separation of variables and explicit integration of the classical Steklov{ Lyapunov systems, which was ¯rst made by F. KÄotter in 1900. Namely, we give a geometric interpretation of the ... 
Sigmafunction solution to the general Somos6 recurrence via hyperelliptic Prym varieties
Fedorov, Yuri; Hone, Andy (Oxford University Press, 20160909)
Article
Open AccessWe construct the explicit solution of the initial value problem for sequences generated by the general Somos6 recurrence relation, in terms of the Kleinian sigmafunction of genus 2. For each sequence there is an associated ... 
SteklovLyapunov type systems
Bolsinov, A. V.; Fedorov, Yuri (2003)
Article
Open AccessIn this paper we describe integrable generalizations of the classical Steklov– Lyapunov systems, which are deﬁned on a certain product so(m) × so(m), as well as the structure of rank r coadjoint orbits in so(m)×so(m). ... 
The hydrodynamic Chaplygin sleigh
Fedorov, Yuri; García Naranjo Ortiz de la Huerta, Luis Constantino (2010)
Article
Open AccessWe consider the motion of rigid bodies in a potential fluid subject to certain nonholonomic constraints and show that it is described by Euler–Poincar´e– Suslov equations. In the twodimensional case, when the constraint ... 
The motion of the 2D hydrodynamic chaplygin sleigh in the presence of circulation
Fedorov, Yuri; García Naranjo, Luis C.; Vankerschaver, Joris (201303)
Article
Open AccessWe consider the motion of a planar rigid body in a potential twodimensional flow with a circulation and subject to a certain nonholonomic constraint. This model can be related to the design of underwater vehicles. ... 
The PicardFuchs equations for complete hyperelliptic integrals of even order curves, and the actions of the generalized Neumann system
Fedorov, Yuri; Pantazi, Chara (20140301)
Article
Open AccessWe consider a family of genus 2 hyperelliptic curves of even order and obtain explicitly the systems of 5 linear ordinary differential equations for periods of the corresponding Abelian integrals of first, second, and third ...