Yuri N. Fedorov
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Yuri N. Fedorov has a total of 19 co-authors. Here are the top co-authors by number of shared publications:
- Bozidar Jovanovic
Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Serbia
5 shared publications - Luis C. Garcia-Naranjo
Dipartimento di Matematica “Tullio Levi-Civita”, Università di Padova, Padova, Italy
5 shared publications - Andrzej J. Maciejewski
Janusz Gil Institute of Astronomy, University of Zielona Gora, Zielona Gora, Poland
4 shared publications - Maria Przybylska
Institute of Physics, University of Zielona Gora, Zielona Gora, Poland
4 shared publications - Andrew N. W. Hone
School of Engineering, Mathematics and Physics, University of Kent, Canterbury, United Kingdom
3 shared publications - Victor Z. Enolskii
Institute of Magnetism 36 Vernadski Str. Kyiv-142 Ukraine
3 shared publications
Latest Publications
- 11 August 2022
- Published by Springer Nature in Israel Journal of Mathematics
- Vol. 250 (1) , 345-402
The sigma function over a family of curves with a singular fiber
- 11 August 2022
- Published by Springer Nature in Israel Journal of Mathematics
- Vol. 250 (1) , 345-402
The sigma function over a family of curves with a singular fiber
- 1 January 2021
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems
- Vol. 41 (6) , 2559-2599
Continuous and discrete Neumann systems on Stiefel varieties as matrix generalizations of the Jacobi–Mumford systems
We study geometric and algebraic geometric properties of the continuous and discrete Neumann systems on cotangent bundles of Stiefel varieties$ V_{n,r} $ . The systems are integrable in the non-commutative sense, and by applying a$ 2r\times 2r $ –Lax representation, we show that generic complex invariant manifolds are open subsets of affine Prym varieties on which the complex flow is linear. The characteristics of the varieties and the direction of the flow are calculated explicitly. Next, we construct a family of multi-valued integrable discretizations of the Neumann systems and describe them as translations on the Prym varieties, which are written explicitly in terms of divisors of points on the spectral curve.- 1 January 2021
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems
- Vol. 41 (6) , 2559-2599
Continuous and discrete Neumann systems on Stiefel varieties as matrix generalizations of the Jacobi–Mumford systems
We study geometric and algebraic geometric properties of the continuous and discrete Neumann systems on cotangent bundles of Stiefel varieties$ V_{n,r} $ . The systems are integrable in the non-commutative sense, and by applying a$ 2r\times 2r $ –Lax representation, we show that generic complex invariant manifolds are open subsets of affine Prym varieties on which the complex flow is linear. The characteristics of the varieties and the direction of the flow are calculated explicitly. Next, we construct a family of multi-valued integrable discretizations of the Neumann systems and describe them as translations on the Prym varieties, which are written explicitly in terms of divisors of points on the spectral curve.- 1 September 2020
- Published by Pleiades Publishing Ltd in Proceedings of the Steklov Institute of Mathematics
- Vol. 310 (1) , 163-174
Discrete Geodesic Flows on Stiefel Manifolds
We study integrable discretizations of geodesic flows of Euclidean metrics on the cotangent bundles of the Stiefel manifolds \(V_{n,r}\). In particular, for \(n=3\) and \(r=2\), after the identification \(V_{3,2}\cong\mathrm{SO}(3)\), we obtain a discrete analog of the Euler case of the rigid body motion corresponding to the inertia operator \(I=(1,1,2)\). In addition, billiard-type mappings are considered; one of them turns out to be the “square root” of the discrete Neumann system on \(V_{n,r}\).- 1 September 2020
- Published by Pleiades Publishing Ltd in Proceedings of the Steklov Institute of Mathematics
- Vol. 310 (1) , 163-174
Discrete Geodesic Flows on Stiefel Manifolds
We study integrable discretizations of geodesic flows of Euclidean metrics on the cotangent bundles of the Stiefel manifolds \(V_{n,r}\). In particular, for \(n=3\) and \(r=2\), after the identification \(V_{3,2}\cong\mathrm{SO}(3)\), we obtain a discrete analog of the Euler case of the rigid body motion corresponding to the inertia operator \(I=(1,1,2)\). In addition, billiard-type mappings are considered; one of them turns out to be the “square root” of the discrete Neumann system on \(V_{n,r}\).- Open Access
Continuous and discrete Neumann systems on Stiefel varieties as matrix generalizations of the Jacobi-Mumford systems
We study geometric and algebraic geometric properties of the continuous and discrete Neumann systems on cotangent bundles of Stiefel varieties $V_{n,r}$. The systems are integrable in the non-commutative sense, and by applying a $2r\times 2r$--Lax representation, we show that generic complex invariant manifolds are open subsets of affine (non-compact) Prym varieties on which the complex flow is linear. The characteristics of the varieties and the direction of the flow are calculated explicitly. Next, we construct a family of (multi-valued) integrable discretizations of the Neumann systems and describe them as translations on the Prym varieties, which are written explicitly in terms of divisors of points on the spectral curve. It appears that the systems inherit or naturally generalize the basic properties of the classical Neumann system on $S^{n-1}$ and, therefore, of the Jacobi--Mumford systems: the structure of the Lax matrices, the spectral curve, the equations of motion, linearization on Abelian varieties, and, in the discrete case, the formula for the translation on them.Open AccessContinuous and discrete Neumann systems on Stiefel varieties as matrix generalizations of the Jacobi-Mumford systems
We study geometric and algebraic geometric properties of the continuous and discrete Neumann systems on cotangent bundles of Stiefel varieties $V_{n,r}$. The systems are integrable in the non-commutative sense, and by applying a $2r\times 2r$--Lax representation, we show that generic complex invariant manifolds are open subsets of affine (non-compact) Prym varieties on which the complex flow is linear. The characteristics of the varieties and the direction of the flow are calculated explicitly. Next, we construct a family of (multi-valued) integrable discretizations of the Neumann systems and describe them as translations on the Prym varieties, which are written explicitly in terms of divisors of points on the spectral curve. It appears that the systems inherit or naturally generalize the basic properties of the classical Neumann system on $S^{n-1}$ and, therefore, of the Jacobi--Mumford systems: the structure of the Lax matrices, the spectral curve, the equations of motion, linearization on Abelian varieties, and, in the discrete case, the formula for the translation on them. - Open Access
- 28 October 2016
- Published by Taylor & Francis in Experimental Mathematics
- Vol. 27 (2) , 147-178
Algebraic Description of Jacobians Isogeneous to Certain Prym Varieties with Polarization (1,2)
For a class of non-hyperelliptic 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 isogeneous to the Prym varieties associated with such coverings. Our description is based on previous studies of Prym varieties with polarization (1,2) in connection with separation of variables in a series of classical and new algebraic integrable systems linearized on such varieties. We also consider some special cases of the covering C → E, in particular, when the corresponding Prym varieties contain pairs of elliptic curves and the Jacobian of C is isogeneous (but not isomorphic) to the product of three different elliptic curves. Our description is accompanied with explicit algorithms of calculation of periods of the Prym varieties and of absolute invariants of genus 2 curves. They are followed by numerical examples, which experimentally confirm main results of the article.
- 28 October 2016
- Published by Taylor & Francis in Experimental Mathematics
- Vol. 27 (2) , 147-178
Open AccessAlgebraic Description of Jacobians Isogeneous to Certain Prym Varieties with Polarization (1,2)
For a class of non-hyperelliptic 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 isogeneous to the Prym varieties associated with such coverings. Our description is based on previous studies of Prym varieties with polarization (1,2) in connection with separation of variables in a series of classical and new algebraic integrable systems linearized on such varieties. We also consider some special cases of the covering C → E, in particular, when the corresponding Prym varieties contain pairs of elliptic curves and the Jacobian of C is isogeneous (but not isomorphic) to the product of three different elliptic curves. Our description is accompanied with explicit algorithms of calculation of periods of the Prym varieties and of absolute invariants of genus 2 curves. They are followed by numerical examples, which experimentally confirm main results of the article.
- Open Access
Sigma-function solution to the general Somos-6 recurrence via hyperelliptic Prym varieties
We construct the explicit solution of the initial value problem for sequences generated by the general Somos-6 recurrence relation, in terms of the Kleinian sigma-function of genus two. For each sequence there is an associated genus two curve $X$, such that iteration of the recurrence corresponds to translation by a fixed vector in the Jacobian of $X$. The construction is based on a Lax pair with a spectral curve $S$ of genus four admitting an involution $\sigma$ with two fixed points, and the Jacobian of $X$ arises as the Prym variety Prym$(S,\sigma)$.Open AccessSigma-function solution to the general Somos-6 recurrence via hyperelliptic Prym varieties
We construct the explicit solution of the initial value problem for sequences generated by the general Somos-6 recurrence relation, in terms of the Kleinian sigma-function of genus two. For each sequence there is an associated genus two curve $X$, such that iteration of the recurrence corresponds to translation by a fixed vector in the Jacobian of $X$. The construction is based on a Lax pair with a spectral curve $S$ of genus four admitting an involution $\sigma$ with two fixed points, and the Jacobian of $X$ arises as the Prym variety Prym$(S,\sigma)$. - Open Access
A shortcut to the Kovalevskaya curve
We present a systematic way of derivation of the algebraic curves of separation of variables for the classical Kovalevskaya top and its generalizations, starting from the spectral curve of the corresponding Lax representation found by Reyman and Semonov-Tian-Shansky. In particular, we show how the known Kovalevskaya curve of separation can be obtained, by a simple one-step transformation, from the spectral curve. The algorithm works for the general constants of motion of the system and is based on W. Barth's description of Prym varieties via pencils of genus 3 curves. It also allows us to derive new curves of separation of variables in various generalizations of this system.
Open AccessA shortcut to the Kovalevskaya curve
We present a systematic way of derivation of the algebraic curves of separation of variables for the classical Kovalevskaya top and its generalizations, starting from the spectral curve of the corresponding Lax representation found by Reyman and Semonov-Tian-Shansky. In particular, we show how the known Kovalevskaya curve of separation can be obtained, by a simple one-step transformation, from the spectral curve. The algorithm works for the general constants of motion of the system and is based on W. Barth's description of Prym varieties via pencils of genus 3 curves. It also allows us to derive new curves of separation of variables in various generalizations of this system.
- Open Access
- 1 September 2015
- Published by Oxford University Press (OUP) in Journal of Integrable Systems
- Vol. 1 (1) , xyw012
Sigma-function solution to the general Somos-6 recurrence via hyperelliptic Prym varieties
We construct the explicit solution of the initial value problem for sequences generated by the general Somos-6 recurrence relation, in terms of the Kleinian sigma-function of genus 2. For each sequence there is an associated genus 2 curve , such that iteration of the recurrence corresponds to translation by a fixed vector in the Jacobian of . The construction is based on a Lax pair with a spectral curve of genus 4 admitting an involution with two fixed points, and the Jacobian of arises as the Prym variety Prym.- 1 September 2015
- Published by Oxford University Press (OUP) in Journal of Integrable Systems
- Vol. 1 (1) , xyw012
Open AccessSigma-function solution to the general Somos-6 recurrence via hyperelliptic Prym varieties
We construct the explicit solution of the initial value problem for sequences generated by the general Somos-6 recurrence relation, in terms of the Kleinian sigma-function of genus 2. For each sequence there is an associated genus 2 curve , such that iteration of the recurrence corresponds to translation by a fixed vector in the Jacobian of . The construction is based on a Lax pair with a spectral curve of genus 4 admitting an involution with two fixed points, and the Jacobian of arises as the Prym variety Prym. - 10 December 2014
- Published by Springer Nature in Journal of Nonlinear Science
- Vol. 25 (1) , 203-246
Unimodularity and Preservation of Volumes in Nonholonomic Mechanics
- 10 December 2014
- Published by Springer Nature in Journal of Nonlinear Science
- Vol. 25 (1) , 203-246
Unimodularity and Preservation of Volumes in Nonholonomic Mechanics
- Open Access
Unimodularity and preservation of volumes in nonholonomic mechanics
The equations of motion of a mechanical system subjected to nonholonomic linear constraints can be formulated in terms of a linear almost Poisson structure in a vector bundle. We study the existence of invariant measures for the system in terms of the unimodularity of this structure. In the presence of symmetries, our approach allows us to give necessary and sufficient conditions for the existence of an invariant volume, that unify and improve results existing in the literature. We present an algorithm to study the existence of a smooth invariant volume for nonholonomic mechanical systems with symmetry and we apply it to several concrete mechanical examples.
Open AccessUnimodularity and preservation of volumes in nonholonomic mechanics
The equations of motion of a mechanical system subjected to nonholonomic linear constraints can be formulated in terms of a linear almost Poisson structure in a vector bundle. We study the existence of invariant measures for the system in terms of the unimodularity of this structure. In the presence of symmetries, our approach allows us to give necessary and sufficient conditions for the existence of an invariant volume, that unify and improve results existing in the literature. We present an algorithm to study the existence of a smooth invariant volume for nonholonomic mechanical systems with symmetry and we apply it to several concrete mechanical examples.