P. Dehornoy, I. Dynnikov, D. Rolfsen, B. Wiest, Ordering braids, Mathematical Surveys and Monographs, 148, American Mathematical Society, Providence, RI, 2008, x+323 pp.
I. Dynnikov, “Arc-presentations of links: monotonic simplification”, Fund. Math., 190 (2006), 29–76
I. A. Dynnikov, “Konechno opredelennye gruppy i polugruppy v teorii uzlov”, Trudy MIAN, 231, 2000, 231–248
I. A. Dynnikov, “Geometriya zon ustoichivosti v zadache S. P. Novikova o poluklassicheskom dvizhenii elektrona”, Uspekhi matematicheskikh nauk, 54:1 (1999), 21–60
S. P. Novikov, I. A. Dynnikov, “Diskretnye spektralnye simmetrii malomernykh differentsialnykh operatorov i raznostnykh operatorov na pravilnykh reshetkakh i dvumernykh mnogoobraziyakh”, UMN, 52:5 (1997), 175–234
Ivan Dynnikov, Maxim Prasolov, “Rectangular diagrams of surfaces: distinguishing Legendrian knots”, J. Topol., 14:3 (2021), 701–860 , arXiv: 1712.06366;
2.
Ivan Dynnikov, Vera Sokolova, “Multiflypes of rectangular diagrams of links”, J. Knot. Theor. Ramif., 30:6 (2021), 2150038 , 15 pp., arXiv: 2009.02247;
3.
I.Dynnikov, V.Shastin, “Distinguishing Legendrian knots with trivial orientation-preserving symmetry group”, Algebraic and Geometric Topology, 2021 (to appear) , arXiv: 1810.06460
4.
Ivan Dynnikov, “Counting intersections of normal curves”, J. Algebra, 2021, 1–51 (Published online) , arXiv: 2010.01638; (Published online)
5.
I. A. Dynnikov, A. Ya. Mal'tsev, Zh. Èksper. Teoret. Fiz., 160:6 (2021), 835–864
2020
6.
Ivan Dynnikov, Pascal Hubert, Alexandra Skripchenko, Dynamical systems around the Rauzy gasket and their ergodic properties, 2020 , 30 pp., arXiv: 2011.15043
7.
Ivan Dynnikov, Maxim Prasolov, “Rectangular diagrams of surfaces: the basic moves”, Proc. Int. Geom. Cent., 13:4 (2020), 50–88 , arXiv: 2011.04995 (cited: 1); ;
8.
A. V. Borisov, I. A. Dynnikov, A. A. Glutsyuk, A. E. Mironov, I. A. Taimanov, A. Yu. Vesnin, “The conference “Dynamics in Siberia”, Novosibirsk, February 24–29, 2020”, Sib. elektron. matem. izv., 17 (2020), 68–96
2019
9.
I. A. Dynnikov, “Transverse-Legendrian links”, Siberian Electronic Mathematicsl Reports, 16 (2019), 1960–1980 , arXiv: 1911.11806
10.
S. P. Novikov, R. De Leo, I. A. Dynnikov, A. Ya. Mal'tsev, “Theory of Dynamical Systems and Transport Phenomena in Normal Metals”, J. Exp. Theor. Phys., 129:4 (2019), 710–721 (cited: 3) (cited: 3)
11.
Ivan Dynnikov, Maxim Prasolov, “Classification of Legendrian Knots of Topological Type $7_6$ with Maximal Thurston–Bennequin Number”, J. Knot. Theor. Ramif., 28:14 (2019), 1950089 , 13 pp., arXiv: 1901.03600 (cited: 1) (cited: 1)
12.
I. A. Dynnikov, D. V. Millionshchikov, Mat. Pros., 23, MCCME, Moscow, 2019, 7–19
13.
I. A. Dynnikov, A. A. Glutsyuk, A. E. Mironov, I. A. Taimanov, A. Yu. Vesnin, “The Conference “Dynamics in Siberia”, Novosibirsk, February 25 – March 2, 2019”, Sib. elektron. matem. izv., 16 (2019), 16–39
2018
14.
I. A. Dynnikov, “Bounded discrete holomorphic functions on the hyperbolic plane”, Proc. Steklov Inst. Math., 302 (2018), 186–197
15.
I. A. Dynnikov, V. A. Shastin, “On equivalence of Legendrian knots”, Russian Math. Surveys, 73:6 (2018), 1125–1127 (cited: 1)
16.
Topologiya i fizika, Sbornik statei. K 80-letiyu so dnya rozhdeniya akademika Sergeya Petrovicha Novikova, Trudy MIAN, 302, ed. V. M. Bukhshtaber, I. A. Dynnikov, O. K. Sheinman, MAIK «Nauka/Interperiodika», M., 2018 , 399 pp.
17.
V. M. Buchstaber, V. A. Vassiliev, A. Yu. Vesnin, I. A. Dynnikov, Yu. G. Reshetnyak, A. B. Sossinsky, I. A. Taimanov, V. G. Turaev, A. T. Fomenko, E. A. Fominykh, A. V. Chernavsky, “Sergei Vladimirovich Matveev (on his 70th birthday)”, Russian Math. Surveys, 73:4 (2018), 737–746
18.
I. A. Dynnikov, A. A. Glutsyuk, G. N. Kulipanov, A. E. Mironov, I. A. Taimanov, A. Yu. Vesnin, “The Conference «Dynamics in Siberia» dedicated to the 90th anniversary of B. V. Chirikov, Novosibirsk, February 26–March 4, 2018”, Sib. elektron. matem. izv., 15 (2018), 10–38
2017
19.
Ivan Dynnikov, Alexandra Skripchenko, “Minimality of interval exchange transformations with restrictions”, J. Mod. Dyn., 11 (2017), 219–248 , arXiv: 1510.03707 (cited: 1) (cited: 1)
20.
I. A. Dynnikov, M. V. Prasolov, “Rectangular diagrams of surfaces: representability”, Sb. Math., 208:6 (2017), 791–841 (cited: 3) (cited: 1)
21.
I. A. Dynnikov, A. A. Glutsyuk, A. E. Mironov, I. A. Taimanov, A. Yu. Vesnin, “The conference “Dynamics in Siberia”, Novosibirsk, February 26–March 4, 2017”, Sib. elektron. matem. izv., 14 (2017), 7–30
2016
22.
I. A. Dynnikov, A. E. Mironov, I. A. Taimanov, A. Yu. Vesnin, “The Conference «Dynamics in Siberia», Novosibirsk, February 29–March 4, 2016”, Sib. elektron. matem. izv., 13 (2016), 1–41 (cited: 1)
I. A. Dynnikov, “On a new discretization of complex analysis”, Russian Math. Surveys, 70:6 (2015), 1031–1050 (cited: 2) (cited: 2)
2014
25.
I. Dynnikov, A. Skripchenko, “On typical leaves of a measured foliated 2-complex of thin type”, Topology, Geometry, Integrable Systems, and Mathematical Physics: Novikov's Seminar 2012–2014, Advances in the Mathematical Sciences, Amer. Math. Soc. Transl. Ser. 2, 234, eds. V. M. Buchstaber, B. A. Dubrovin, I. M. Krichever, Amer. Math. Soc., Providence, RI, 2014, 173–200 , arXiv: 1309.4884
2013
26.
I. A. Dynnikov, M. V. Prasolov, “Bypasses for rectangular diagrams. A proof of the Jones conjecture and related questions”, Trans. Moscow Math. Soc., 2013 (2013), 97–144 (cited: 20)
27.
I. A. Dynnikov, V. A. Shastin, “On independence of some pseudocharacters on braid groups”, St. Petersburg Math. J., 24:6 (2013), 863–876 (cited: 1) (cited: 1)
2009
28.
R. DeLeo, I. A. Dynnikov, “Geometry of plane sections of the infinite regular skew polyhedron $\{4,6\mid 4\}$”, Geom. Dedicata, 138:1 (2009), 51–67 (cited: 18) (cited: 4) (cited: 19)
2008
29.
I. A. Dynnikov, “Interval Identification Systems and Plane Sections of 3-Periodic Surfaces”, Proc. Steklov Inst. Math., 263 (2008), 65–77 (cited: 10) (cited: 4) (cited: 4) (cited: 10)
30.
P. Dehornoy, I. Dynnikov, D. Rolfsen, B. Wiest, Ordering braids, Math. Surveys Monogr., 148, Amer. Math. Soc., Providence, RI, 2008 , x+323 pp.
2007
31.
R. De Leo, I. A. Dynnikov, “An example of a fractal set of plane directions having chaotic intersections with a fixed 3-periodic surface”, Russian Math. Surveys, 62:5 (2007), 990–992 (cited: 7) (cited: 8)
32.
I. Dynnikov, B. Wiest, “On the complexity of braids”, J. Eur. Math. Soc. (JEMS), 9:4 (2007), 801–840 (cited: 23) (cited: 13) (cited: 27)
2006
33.
I. A. Dynnikov, “Arc-presentations of links: monotonic simplification”, Fund. Math., 190 (2006), 29–76 (cited: 46) (cited: 29) (cited: 52)
2005
34.
I. A. Dynnikov, S. P. Novikov, “Topology of quasi-periodic functions on the plane”, Russian Math. Surveys, 60:1 (2005), 1–26 (cited: 9) (cited: 4) (cited: 4) (cited: 10)
2004
35.
I. A. Dynnikov, “Finitely presented semigroups in knot theory. Oriented case”, Geometry, topology, and mathematical physics, Amer. Math. Soc. Transl. Ser. 2, 212, Amer. Math. Soc., Providence, RI, 2004, 133–144
2003
36.
I. A. Dynnikov, S. P. Novikov, “Geometry of the triangle equation on two-manifolds”, Mosc. Math. J., 3:2 (2003), 419–438 (cited: 26) (cited: 27) (cited: 17)
37.
I. A. Dynnikov, “Recognition algorithms in knot theory”, Russian Math. Surveys, 58:6 (2003), 1093–1139 (cited: 6) (cited: 6) (cited: 5)
2002
38.
I. A. Dynnikov, S. V. Smirnov, “Exactly soluble cyclic Darboux $q$-chains”, Russian Math. Surveys, 57:6 (2002), 1218–1219 (cited: 1) (cited: 1)
39.
I. A. Dynnikov, “On a Yang–Baxter map and the Dehornoy ordering”, Russian Math. Surveys, 57:3 (2002), 592–594 (cited: 21) (cited: 13) (cited: 23)
40.
P. Dehornoy, I. Dynnikov, D. Rolfsen, B. Wiest, Why are braids orderable?, Panor. Syntheses, 14, Société Mathématique de France, Paris, 2002 , xiv+190 pp.
2001
41.
I. A. Dynnikov, “A new way to represent links, one-dimensional formalism and untangling technology”, Acta Appl. Math., 69:3 (2001), 243–283 (cited: 3) (cited: 4) (cited: 4)
2000
42.
I. A. Dynnikov, “Three-Page Approach to Knot Theory. Universal Semigroup”, Funct. Anal. Appl., 34:1 (2000), 24–32 (cited: 8) (cited: 8)
43.
I. A. Dynnikov, “Finitely Presented Groups and Semigroups in Knot Theory”, Proc. Steklov Inst. Math., 231 (2000), 220–237
1999
44.
I. A. Dynnikov, “Three-Page Approach to Knot Theory. Encoding and Local Moves”, Funct. Anal. Appl., 33:4 (1999), 260–269 (cited: 5) (cited: 7)
45.
I. A. Dynnikov, “The geometry of stability regions in Novikov's problem on the semiclassical motion of an electron”, Russian Math. Surveys, 54:1 (1999), 21–59 (cited: 27) (cited: 15) (cited: 28)
1998
46.
I. A. Dynnikov, “Three-page representation of links”, Russian Math. Surveys, 53:5 (1998), 1091–1092 (cited: 2)
47.
I. Dynnikov, “Surfaces in 3-torus: geometry of plane sections”, European Congress of Mathematics, Vol. I (Budapest, 1996), Progr. Math., 168, Birkhäuser, Basel, 1998, 162–177
1997
48.
I. A. Dynnikov, S. P. Novikov, “Laplace transforms and simplicial connections”, Russian Math. Surveys, 52:6 (1997), 1294–1295 (cited: 4) (cited: 5)
49.
S. P. Novikov, I. A. Dynnikov, “Discrete spectral symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds”, Russian Math. Surveys, 52:5 (1997), 1057–1116 (cited: 46) (cited: 44)
50.
I. A. Dynnikov, “The Alexander polynomial in several variables can be expressed in terms of the Vassiliev invariants”, Russian Math. Surveys, 52:1 (1997), 219–221
51.
I. A. Dynnikov, “Semiclassical motion of the electron. A proof of the Novikov conjecture in general position and counterexamples”, Solitons, geometry, and topology: on the crossroad, Amer. Math. Soc. Transl. Ser. 2, 179, Amer. Math. Soc., Providence, RI, 1997, 45–73
52.
A. P. Veselov, I. A. Dynnikov, “Integrable gradient flows and Morse theory”, St. Petersburg Math. J., 8:3 (1997), 429–446
1999
53.
I. A. Dynnikov, “Semiclassical electron motion and Novikov's conjecture”, J. Math. Sci. (New York), 94:4 (1999), 1589–1592
1994
54.
I. A. Dynnikov, “Intersections of level surfaces of pseudoperiodic functions”, Russian Math. Surveys, 49:1 (1994), 229–230 (cited: 1) (cited: 2)
1993
55.
I. A. Dynnikov, “Proof of S. P. Novikov's conjecture on the semiclassical motion of an electron”, Math. Notes, 53:5 (1993), 495–501 (cited: 12) (cited: 6) (cited: 17)
56.
I. A. Dynnikov, “S. P. Novikov's problem on the semiclassical motion of an electron”, Russian Math. Surveys, 48:2 (1993), 173–174 (cited: 1)
1992
57.
I. A. Dynnikov, “Proof of S. P. Novikov's conjecture for the case of small perturbations of rational magnetic fields”, Russian Math. Surveys, 47:3 (1992), 172–173 (cited: 8) (cited: 15)
58.
I. A. Dynnikov, “Homotopic classification of spherical spatial forms”, Moscow Univ. Math. Bull., 47:5 (1992), 1–6
Presentations in Math-Net.Ru
1.
Сравнение лежандровых узлов I. A. Dynnikov Scientific session of the Steklov Mathematical Institute of RAS dedicated to the results of 2021 November 24, 2021 15:00
2.
Слова Арну–Рози. Лекция И. А. Дынников Summer School "Contemporary Mathematics" Named After Vitaly Arnold, 2021 July 21, 2021 15:30
Выпуклые поверхности в смысле Жиру и зеркальные диаграммы I. A. Dynnikov Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS November 8, 2017 18:30
Гомологии Хованова II I. A. Dynnikov Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS January 12, 2011 14:00
71.
Гомологии Хованова I I. A. Dynnikov Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS January 8, 2011 12:00
Discretization of complex analysis S. P. Novikov, I. A. Dynnikov International Conference "Differential Equations and Topology" dedicated to the Centennial Anniversary of L. S. Pontryagin June 22, 2008 12:20
Топология квазипериодических функций I. A. Dynnikov Seminar of the Department of Geometry and Topology "Geometry, Topology and Mathematical Physics", Steklov Mathematical Institute of RAS November 3, 2004
Topology and physics, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 302, ed. V. M. Buchstaber, I. A. Dynnikov, O. K. Sheinman, 2018, 399 с. http://mi.mathnet.ru/book1715
2021
Terms of Use