Ivan A. DYNNIKOV

Researcher at the Laboratory from Oct 2002 to Jun 2003

Publications

1. I.A.Dynnikov. Recognition algorithms in knot theory. (Russian) Uspekhi Mat. Nauk 58 (2003), no. 6, 45--92; translation in Russian Math. Surveys 58 (2003), no. 6.
2. I.A.Dynnikov and S.P.Novikov. Geometry of the triangle equation on two-manifolds. Moscow Math. Journal 3 (2003), no. 2, 419--438.
3. P.Dehornoy, I.Dynnikov, D.Rolfsen, and B.Wiest. Why are braids orderable? Panoramas et Synthèses 14, SMF 2002, pp. 190+xiii.
4. I.A.Dynnikov and S.V.Smirnov. Exactly solvable cyclic Darboux q-chains. (Russian) Uspekhi Mat. Nauk 57 (2002), no. 6, 183--184; translation in Russian Math. Surveys 57 (2002), no. 6, 1218--1219.
5. I.A.Dynnikov. Arc-presentation of links. Monotonic simplification. Preprint, http://arxiv.org/abs/math.gt/0208153, pp. 38.
6. I.A.Dynnikov. On a Yang-Baxter mapping and the Dehornoy ordering. (Russian) Uspekhi Mat. Nauk 57 (2002), no. 3(345), 151--152; translation in Russian Math. Surveys 57 (2002), no. 3, 592--594.
7. I.A.Dynnikov. A new way to represent links, one-dimensional formalism and untangling technology. Acta Appl. Math. 69 (2001), no. 3, 243--283.
8. I.A.Dynnikov. Finitely presented groups and semigroups in knot theory. Tr. Mat. Inst. Steklova 231 (2000), 231--248; translation in Proc. Steklov Inst. Math. 231 (2000), 220--237.
9. I.A.Dynnikov. Three-page approach to knot theory. Universal semigroup. (Russian) Funktsional'nyi Analiz i Ego Prilozhenija 34 (2000), no. 1, 29--40; translation in Functional Analysis and Its Appl. 34 (2000), no. 1, 24--32.
10. I.A.Dynnikov. Three-page approach to knot theory. Encoding and local moves. (Russian) Funktsional'nyi Analiz i Ego Prilozhenija 33 (1999), no. 4, 25--37; translation in Functional Analysis and Its Appl. 33 (1999), no. 4, 260--269.
11. I.A.Dynnikov. Geometry of the stability zones in the Novikov problem on the semiclassical motion of the electron. (Russian) Uspekhi Mat. Nauk 54 (1999), no. 1, 21--60.
12. I.A.Dynnikov. Three-page link presentation. (Russian) Uspekhi Mat. Nauk 53 (1998), no. 5, 237--238; translation in Russian Math. Surveys 53 (1998), no. 5, 1091--1092.
13. I.A.Dynnikov. Surfaces in 3-Torus: Geometry of Plane Sections. In 2nd European Congress of Math. Proc. (Budapest, July, 1996), Progress in Math., 168, 162--177. Birkhauser Verlag Basel, 1998.
14. I.A.Dynnikov and A.Ya.Mal'tsev. Topological characteristics of electron spectra in monocrystals. (Russian) Zh. Eksp. Teor. Fiz., 112:1 (1997), 371--378; translation in J.E.T.P 85:1 (1997), 205--208.
15. I.A.Dynnikov and S.P.Novikov. Laplace transformations and simplicial connections. (Russian) Uspekhi Mat. Nauk 52 (1997), no. 6(318), 157--158; translation in Russian Math. Surveys 52 (1997), no. 6, 1294--1295.
16. S.P.Novikov and I.A.Dynnikov. Discrete spectral symmetries of low-dimensional differential operators and difference operators on lattices and two-manifolds. (Russian) Uspekhi Mat. Nauk 52 (1997), no. 5(317), 175--234; translation in Russian Math. Surveys 52 (1997) no. 5, 1057--1116.
17. I.A.Dynnikov. The Alexander polynomial in several variables expressed in terms of Vassiliev invariants. (Russian) Uspekhi Mat. Nauk 52 (1997), no. 1(313), 227--228; translation in Russian Math. Surveys 52 (1997), no. 1, 219--221.
18. I.A.Dynnikov. Semiclassical motion of the electron. A proof of the Novikov conjecture in general position and counterexamples. In: Solitons, geometry, and topology: on the crossroad, 45--73, Amer. Math. Soc. Transl. Ser. 2, 179, Amer. Math. Soc., Providence, RI, 1997.
19. I.A.Dynnikov and A.P.Veselov. Integrable gradient flows and Morse theory. (Russian) Algebra i Analiz 8 (1996), no. 3, 78--103; translation in St. Petersburg Math. J. 8 (1997), no. 3, 429--446.
20. I.A.Dynnikov. Intersections of level surfaces of pseudoperiodic functions. (Russian). Uspekhi Mat. Nauk 49 (1994), no. 1(295), 213--214.
21. I.A.Dynnikov. A proof of the conjecture of S.P.Novikov on the semiclassical motion of an electron. (Russian) Mat. Zametki 53 (1993), no. 5, 57--68; translation in Math Notes 53 (1993), no. 5--6, 495--501.
22. I.A.Dynnikov. S.P.Novikov's problem on the semiclassical motion of an electron. (Russian) Uspekhi Mat. Nauk 48 (1993), no. 2(290), 179--180; translation in Russian Math. Surveys 48 (1993), no. 2, 173--174.
23. I.A.Dynnikov. A proof of S.P.Novikov's conjecture for the case of small perturbations of rational magnetic fields. (Russian) Uspekhi Mat. Nauk 47 (1992), no. 3(285), 161--162; translation in Russian Math. Surveys 47 (1992), no. 3, 172--173.
24. I.A.Dynnikov. Homotopy classification of spherical space forms. (Russian) Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1992, no. 5, 3--8, 104; translation in Moscow Univ. Math. Bull. 47 (1992), no. 5, 1--6.