dynamical systems,
Hamiltonian systems,
topological conjugacy of Hamiltonian systems, periodic solutions, symplectic invariants, low-dimensional topology,
coincidence theory on surfaces,
Morse theory, singularities of integrable Hamiltonian systems
Main publications:
E. A. Kudryavtseva, “Hidden toric symmetry and structural stability of singularities in integrable systems”, Published online 25 October 2021, European Journal of Mathematics, 8 (2022), 1487–1549view pdf, arXiv: 2008.01067
Alexey Bolsinov, Lorenzo Guglielmi, Elena Kudryavtseva, “Symplectic invariants for parabolic orbits and cusp singularities of integrable systems”, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 376:2131 (2018), 20170424 , 29 pp., arXiv: 1802.09910
E. A. Kudryavtseva, “Helicity is the Only Invariant of Incompressible Flows whose Derivative is Continuous in the $C^1$ Topology”, Math. Notes, 99:4 (2016), 611–615math.DS/1511.03746
E. A. Kudryavtseva, “Topology of the spaces of functions with prescribed singularities on surfaces”, Doklady Mathematics, 93:3 (2016), 264–266math.GT/1601.02283
O. V. Bogopolski, E. A. Kudryavtseva, H. Zieschang, “Simple curves on surfaces and an analog of a theorem of Magnus for surface groups”, Math. Z., 247:3 (2004), 595–609
D. L. Gonçalves, E. A. Kudryavtseva, H. Zieschang, “Roots of mappings on nonorientable surfaces and equations in free groups”, Manuscripta Math., 107:3 (2002), 311–341
I. F. Kobtsev, E. A. Kudryavtseva, “Bifurcations of magnetic geodesic flows on surfaces of revolution”, Russian Journal of Mathematical Physics, 32:1 (2025), 1–32 (to appear) , arXiv: 2502.06977
2024
2.
E. A. Kudryavtseva, L. M. Lerman, “Bifurcations in integrable systems with three degrees of freedom — I”, Mathematical Aspects of Mechanics, Collected papers. Dedicated to Dmitry Valerevich Treschev on the occasion of his 60th birthday and to Sergey Vladimirovich Bolotin on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 327, Steklov Math. Inst., Moscow, 2024 (to appear)
3.
A. Yu. Konyaev, E. A. Kudryavtseva, V. I. Sidel'nikov, “Geometry and topology of two-dimensional symplectic manifolds with generic singularities and Hamiltonian systems on them”, Moscow University Mathematics Bulletin, 79:5 (2024), 230–243view pdf
4.
A. Z. Ali, V. A. Kibkalo, E. A. Kudryavtseva, M. V. Onufrienko, “Bifurcations in integrable Hamiltonian systems near corank-one singularities”, Differential Equations, 60:10 (2024), 1311–1368view pdf
2023
5.
E. A. Kudryavtseva, M. V. Onufrienko, “Classification of singularities of smooth functions with a finite cyclic symmetry group”, Russian Journal of Mathematical Physics, 30:1 (2023), 76–94view pdf
E. A. Kudryavtseva, “Hidden toric symmetry and structural stability of singularities in integrable systems”, Published online 25 October 2021, European Journal of Mathematics, 8 (2022), 1487–1549view pdf, arXiv: 2008.01067
E. A. Kudryavtseva, A. A. Oshemkov, “Structurally stable nondegenerate singularities of integrable systems”, Russian Journal of Mathematical Physics, 29:1 (2022), 57–75view pdf, arXiv: 2112.00130
E. Kudryavtseva, N. Martynchuk, “Existence of a smooth Hamiltonian circle action near parabolic orbits and cuspidal tori”, Regular and Chaotic Dynamics, 26:6 (2021), 732–741view pdf, arXiv: 2106.04838
E. A. Kudryavtseva, A. A. Oshemkov, “Bifurkatsii integriruemykh mekhanicheskikh sistem s magnitnym polem na poverkhnostyakh vrascheniya”, Chebyshevskii sbornik, 21:2 (2020), 244–265
A. Bolsinov, N. Dobrovol'skii, A. Ivanov, E. Kudryavtseva, A. Oshemkov, F. Popelenskii, A. Tuzhilin, V. Chubarikov, A. Shafarevich, Chebyshevskii Sb., 21:2 (2020), 5–7
2021
11.
E. A. Kudryavtseva, S. A. Podlipaev, “Superintegrable Bertrand magnetic geodesic flows”, Journal of Mathematical Sciences, 259:5 (2021), 689–698view pdf, arXiv: 2001.05067
2020
12.
E. A. Kudryavtseva, D. A. Fedoseev, “Superintegrable Bertrand natural mechanical systems”, Journal of Mathematical Sciences, 248:4 (2020), 409–429view pdf
2018
13.
Natalia A. Viana Bedoya, Daciberg Lima Gonçalves, Elena A. Kudryavtseva, “Indecomposable branched coverings over the projective plane by surfaces M with χ(M)≤0”, Journal of Knot Theory and Its Ramifications, 27:5 (2018), 1850030 , 23 pp., arXiv: 1702.01822
Alexey Bolsinov, Lorenzo Guglielmi, Elena Kudryavtseva, “Symplectic invariants for parabolic orbits and cusp singularities of integrable systems”, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 376:2131 (2018), 20170424 , 29 pp., arXiv: 1802.09910
E. A. Kudryavtseva, “Continuous orbital invariants of integrable Hamiltonian systems”, Lobachevskii Journal of Mathematics, 38:6 (2017), 1027–1041
2016
16.
D. A. Fedoseev, E. A. Kudryavtseva, “On Bertrands manifolds with equators”, Moscow Univ. Math. Bull., 71:1 (2016), 23–26
17.
E. A. Kudryavtseva, “Helicity is the Only Invariant of Incompressible Flows whose Derivative is Continuous in the $C^1$ Topology”, Math. Notes, 99:4 (2016), 611–615math.DS/1511.03746
18.
P. M. Akhmet'ev, E. A. Kudryavtseva, A. Yu. Smirnov, “A generalization of the Arnol'd inequality in MHD”, Magnetohydrodynamics, 52:1 (2016), 5–14
19.
E. A. Kudryavtseva, “Topology of the spaces of functions with prescribed singularities on surfaces”, Doklady Mathematics, 93:3 (2016), 264–266math.GT/1601.02283
2015
20.
E. A. Kudryavtseva, D. A. Fedoseev, “Mechanical systems with closed orbits on manifolds of revolution”, Sb. Math., 206:5 (2015), 718–737
21.
E. A. Kudryavtseva, “Multipliers of periodic Hill solutions in the theory of moon motion and an averaging method”, Moscow Univ. Math. Bull., 70:4 (2015), 160–170
2017
22.
E. A. Kudryavtseva, “Liouville integrable generalized billiard flows and Poncelet type theorems”, Journal of Mathematical Sciences, 225:4 (2017), 611–638view pdf
2014
23.
E. A. Kudryavtseva, “Conjugation Invariants on the Group of Area-Preserving Diffeomorphisms of the Disk”, Math. Notes, 95:6 (2014), 877–880
2013
24.
E. A. Kudryavtseva, “On the homotopy type of spaces of Morse functions on surfaces”, Sb. Math., 204:1 (2013), 75–113
25.
A. T. Fomenko, E. A. Kudryavtseva, “Each finite group is a symmetry group of some map (an “atom”–bifurcation)”, Moscow Univ. Math. Bull., 68:3 (2013), 148–155
2012
26.
E. A. Kudryavtseva, “Connected components of spaces of Morse functions with fixed critical points”, Moscow Univ. Math. Bull., 67:1 (2012), 1–10
27.
S. I. Bogataya, S. A. Bogatyi, E. A. Kudryavtseva, “An inverse theorem on ‘economic’ maps”, Sb. Math., 203:4 (2012), 554–568
28.
E. A. Kudryavtseva, “Special framed Morse functions on surfaces”, Moscow Univ. Math. Bull., 67:4 (2012), 151–157
29.
E. A. Kudryavtseva, “An analogue of the Liouville theorem for integrable Hamiltonian systems with incomplete flows”, Doklady Mathematics, 86:1 (2012), 527–529 , arXiv: math.DG/1203.5455
30.
E. A. Kudryavtseva, “The Topology of Spaces of Morse Functions on Surfaces”, Math. Notes, 92:2 (2012), 219–236
31.
O. A. Zagryadskii, E. A. Kudryavtseva, D. A. Fedoseev, “A generalization of Bertrand's theorem to surfaces of revolution”, Sb. Math., 203:8 (2012), 1112–1150
32.
E. A. Kudryavtseva, A. T. Fomenko, “Symmetries groups of nice Morse functions on surfaces”, Doklady Mathematics, 86:2 (2012), 691–693
33.
S. A. Bogatyi, E. A. Kudryavtseva, Kh. Tsishang, “O peresecheniyakh zamknutykh krivykh na poverkhnostyakh”, Trudy Sem. vekt. tenz. analizu, XXVIII, 2012, 86–118 , arXiv: math.GT/1111.5277
2011
34.
E. A. Kudryavtseva, T. A. Lepskii, “The topology of Lagrangian foliations of integrable systems with hyperelliptic Hamiltonian”, Sb. Math., 202:3 (2011), 373–411
35.
E. A. Kudryavtseva, “On the topology of the spaces of Morse functions on surfaces”, International conference “Differential equations and related topics” dedicated to Ivan G. Petrovskii. XXIII joint session of Petrovskii Seminar and Moscow Math. Soc. Book of abstracts (Moscow, May 30 – June 4, 2011), M. V. Lomonosov Moscow State University, V. A. Steklov Mathematical Institute RAS, 2011, 69–71
36.
E. A. Kudryavtseva, T. A. Lepskii, “Integriruemye gamiltonovy sistemy s nepolnymi potokami i mnogougolniki Nyutona”, Sovrem. Probl. Matem. Mekhan., VI:3 (2011), 42–55 , arXiv: math.DG/1107.1911
37.
E. A. Kudryavtseva, T. A. Lepskii, “Topologiya sloeniya i teorema Liuvillya dlya integriruemykh sistem s nepolnymi potokami”, Trudy Sem. vekt. tenz. analizu, XXVII, 2011, 106–149
2010
38.
E. A. Kudryavtseva, D. A. Permyakov, “Framed Morse functions on surfaces”, Sb. Math., 201:4 (2010), 501–567
2009
39.
E. A. Kudryavtseva, “Uniform Morse lemma and isotope Morse functions on surfaces”, Moscow Univ. Math. Bull., 64:4 (2009), 150–158
40.
E. A. Kudryavtseva, I. M. Nikonov, A. T. Fomenko, “Symmetric and irreducible abstract polyhedra”, V. A. Sadovnichiy Anniv. Coll. Articles, Contemporary Problems of Mathematics and Mechanics, III, no. 2, 2009, 58–97 (Russian)
41.
D. Andrica, L. Funar, E. A. Kudryavtseva, “On the minimal number of critical points of smooth maps between closed manifolds”, Russian Journal of Mathematical Physics, 16:3 (2009), 363–370
E. A. Kudryavtseva, I. M. Nikonov, A. T. Fomenko, “Maximally symmetric cell decompositions of surfaces and their coverings”, Sb. Math., 199:9 (2008), 1263–1353
43.
S. A. Bogatyi, J. Fricke, E. A. Kudryavtseva, “On multiplicity of mappings between surfaces”, The Zieschang Gedenkschrift, Geometry and Topology Monographs, 14, ed. M. Boileau et al., Geometry & Topology Publications, Coventry, 2008, 49–62 , arXiv: math.GT/0904.1197
D. L. Gonçalves, E. A. Kudryavtseva, H. Zieschang, “Some quadratic equations in the free group of rank 2”, The Zieschang Gedenkschrift, Geometry and Topology Monographs, 14, ed. M. Boileau et al., Geometry & Topology Publications, Coventry, 2008, 219–294 , arXiv: math.GR/0904.1421
45.
E. A. Kudryavtseva, K. Varadarajan, P. Zvengrowski, “Stable inverses of vector bundles and $K$-theory”, JP J. Geom. Top., 8:2 (2008), 129–150
46.
E. A. Kudryavtseva, I. M. Nikonov, A. T. Fomenko, “Maksimalno simmetrichnye kletochnye razbieniya poverkhnostei i ikh nakrytiya”, Mezhdunarodnaya konferentsiya «Differentsialnye uravneniya i topologiya», posvyaschennaya 100-letiyu so dnya rozhdeniya Lva Semenovicha Pontryagina, Tezisy dokladov (Moskva, 17–22 iyunya 2008 g.), Matematicheskii in-t im. V. A. Steklova RAN, Moskovskii gosudarstvennyi universitet im. M. V. Lomonosova, 2008, 471
2006
47.
E. A. Kudryavtseva, E. L. Lakshtanov, “Classification of singularities and bifurcations of critical points of even functions”, Topological Methods in the Theory of Integrable Systems, eds. A. V. Bolsinov, A. T. Fomenko, A. A. Oshemkov, Cambridge Scientific Publishers, Cambridge, 2006, 173–214math.DG/1212.4302
2005
48.
D. L. Gonçalves, E. A. Kudryavtseva, H. Zieschang, “An algorithm for minimal number of intersection points of curves on surfaces”, Proc. Seminar on Vector and Tensor Analysis, 26, 2005, 139–167
49.
E. A. Kudryavtseva, F. Saidak, P. Zvengrowski, “Riemann and his zeta function”, Morfismos, 9:2 (2005), 1–48
2004
50.
S. A. Bogatyi, D. L. Gonçalves, E. A. Kudryavtseva, H. Zieschang, “Minimal Number of Preimages Under Maps of Surfaces”, Math. Notes, 75:1 (2004), 13–18
51.
S. A. Bogatyi, E. A. Kudryavtseva, H. Zieschang, “On the Coincidence Points of Mappings of the Torus into a Surface”, Proc. Steklov Inst. Math., 247 (2004), 9–27
52.
O. V. Bogopolski, E. A. Kudryavtseva, H. Zieschang, “Simple curves on surfaces and an analog of a theorem of Magnus for surface groups”, Math. Z., 247:3 (2004), 595–609
S. A. Bogatyi, D. L. Gonçalves, E. A. Kudryavtseva, H. Zieschang, “Realization of primitive branched coverings over closed surfaces”, Advances in Topological Quantum Field Theory, NATO Sci. Ser. II Math. Phys. Chem., 179, ed. J. M. Bryden, Kluwer Academic Publishers, Dordrecht, 2004, 297–316
2003
54.
S. A. Bogatyi, D. L. Gonçalves, E. A. Kudryavtseva, H. Zieschang, “On the Wecken property for the root problem of mappings between surfaces”, Mosc. Math. J., 3:4 (2003), 1223–1245
E. A. Kudryavtseva, R. Weidmann, H. Zieschang, “Quadratic equations in free groups and topological applications”, Recent advances in group theory and low-dimensional topology (Pusan, 2000), Research and exposition in mathematics, 27, eds. J. Mennike and Jung Rae Cho, Heldermann, Lemgo, 2003, 83–122
56.
S. A. Bogatyi, D. L. Gonçalves, E. A. Kudryavtseva, H. Zieschang, “Realization of primitive branched coverings over closed surfaces following the Hurwitz approach”, Central Europ. J. of Math., 1:2 (2003), 184–197 (electronic)
D. L. Gonçalves, E. A. Kudryavtseva, H. Zieschang, “Roots of mappings on nonorientable surfaces and equations in free groups”, Manuscripta Math., 107:3 (2002), 311–341
C. Hayat-Legrand, E. A. Kudryavtseva, S. Wang, H. Zieschang, “Degrees of self-mappings of Seifert manifolds with finite fundamental groups”, Rendiconti Istit. Mat. Univ. Trieste, 32:1 (2001), 131–147
59.
D. L. Gonçalves, E. A. Kudryavtseva, H. Zieschang, “Intersection index of curves on surfaces and applications to quadratic equations in free groups”, Atti Sem. Mat. Fis. Univ. Modena, IL (2001), 339–400
60.
E. A. Kudryavtseva, “Periodic solutions of the $N$-body problem and applications to planet systems with satellites”, International conference “Differential equations and related topics” dedicated to the Centenary Anniv. of Ivan G. Petrovskii. XX joint session of Petrovskii Seminar and Moscow Math. Soc. Book of abstracts. (Moscow, May 22–27, 2001), Moscow M. V. Lomonosov State University, V. A. Steklov Mathematical Institute RAS, 2001, 221–222
1999
61.
E. A. Kudryavtseva, “Realization of smooth functions on surfaces as height functions”, Sb. Math., 190:3 (1999), 349–405
62.
E. A. Kudryavtseva, “Reduction of Morse functions on surfaces to canonical form by smooth deformation”, Regular and Chaotic Dynamics, 4:3 (1999), 53–60
Yu. A. Brailov, E. A. Kudryavtseva, “Stable topological nonconjugacy of Hamiltonian systems on two-dimensional surfaces”, Moscow Univ. Math. Bull., 54:2 (1999), 20–27
64.
E. A. Kudryavtseva, “Periodic motions of a planetary system with double planets. The generalized Hill problem”, Moscow Univ. Math. Bull., 54:4 (1999), 39–41
65.
E. A. Kudryavtseva, “Canonical form of Reeb graph for Morse functions on surfaces. Inversion of 2-sphere in 3-space”, International Journal of Shape Modeling, 5:1 (1999), 69–80
M. L. Gerver, E. A. Kudryavtseva, “Extremal properties of discrete measures, the universal sequence, and the duality principle”, Sb. Math., 189:11 (1998), 1587–1610
67.
M. L. Gerver, E. A. Kudryavtseva, “Extremal properties of discrete measures, a universal sequence, and the duality principle”, Dokl. Math., 58:3 (1998), 436–439
68.
E. A. Kudryavtseva, “Stable conjugation invariants of Hamiltonian systems on two-dimensional surfaces”, Soviet Math. Dokl., 58:1 (1998), 67–70
69.
E. A. Kudryavtseva, “Ustoichivye topologicheskie i gladkie invarianty sopryazhennosti gamiltonovykh sistem na poverkhnostyakh”, Topologicheskie metody v teorii gamiltonovykh sistem, eds. A. T. Fomenko, A. V. Bolsinov, Faktorial, M., 1998, 147–202
70.
E. A. Kudryavtseva, “Generalization of geometric Poincaré theorem for small perturbations”, Regular and Chaotic Dynamics, 3:2 (1998), 46–66
E. A. Kudryavtseva, N. N. Nekhoroshev, “Periodicheskie traektorii, ostayuschiesya posle raspada semeistv takikh traektorii pri vozmuschenii sistem obyknovennykh differentsialnykh uravnenii”, Sovmestnye zasedaniya seminara im. I. G. Petrovskogo i Moskovskogo matematicheskogo obschestva (XIX sessiya) (Moskva, 20–24 yanv. 1998), Uspekhi mat. nauk, 53, no. 4, 1998, 206–207
M. L. Gerver, E. A. Kudryavtseva, “A new proof of theorems on a universal sequence and extremal properties of discrete measures”, Russian Math. Surveys, 52:6 (1997), 1298–1299
73.
M. L. Gerver, E. A. Kudryavtseva, “A universal sequence in the classical travel-time inversion problem”, Sb. Math., 188:4 (1997), 483–536
74.
M. L. Gerver, E. A. Kudryavtseva, “Extremal properties of wave quides with a finite number of layers in inverse travel-time problems”, Dokl. Math., 56:2 (1997), 777–780
1996
75.
M. L. Gerver, E. A. Kudryavtseva, “On the solution set boundary in the travel-time inversion problem”, Transl. Dokl. Russian Acad. Sci. Earth Sci. Sect., 347:2 (1996), 262–264
1995
76.
M. L. Gerver, E. A. Kudryavtseva, “A theorem on order relations generated by totally positive kernels”, Sb. Math., 186:9 (1995), 1241–1269
77.
M. L. Gerver, E. A. Kudryavtseva, “On the boundary of the set of solutions in travel time inversion and on extremal properties of waveguides with a finite number of layers”, IUGG XXI General Assembly. Abstracts. Week B (Boulder, Colorado. July 2–14), 1995, B10 (UB31B-7)
78.
E. A. Kudryavtseva, M. L. Gerver, “An Algorithm Yielding the Universal Sequence $U$ in travel Time Inversion”, IUGG XXI General Assembly. Abstracts. Week B (Boulder, Colorado. July 2–14), 1995, B11 (UB31B-13)
1994
79.
M. L. Gerver, E. A. Kudryavtseva, “Klassifikatsiya perestanovok uslovno skhodyaschikhsya ryadov”, Shestaya letnyaya konferentsiya turnira gorodov, ITsTG, M., 1994, 20–25, 57–65