## Dynnikov, Ivan Alekseevich

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 Author ID: dynnikov.ivan-alekseevich Published as: Dynnikov, I. A.; Dynnikov, Ivan; Dynnikov, Ivan A.; Dynnikov, Ivan Alekseevich; Dynnikov, I. more...less
 Documents Indexed: 50 Publications since 1992, including 2 Books 2 Contributions as Editor Co-Authors: 26 Co-Authors with 28 Joint Publications 1,165 Co-Co-Authors
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### Co-Authors

 24 single-authored 5 Prasolov, Maxim V. 4 Novikov, Sergeĭ Petrovich 4 Taimanov, Iskander Asanovich 4 Vesnin, Andrei Yu. 3 Mironov, Andreĭ Evgen’evich 3 Skripchenko, Alexandra 3 Wiest, Bertold 2 De Leo, Roberto 2 Dehornoy, Patrick 2 Rolfsen, Dale 2 Shastin, Vladimir Alekseevich 2 Veselov, Alexander Petrovich 1 Andreeva, Maria V. 1 Bukhshtaber, Viktor Matveevich 1 Chernavskiĭ, Alekseĭ Viktorovich 1 Fomenko, Anatoliĭ Timofeevich 1 Fominykh, Evgeny Anatol’evich 1 Kulipanov, Gennadiĭ Nikolaevich 1 Polthier, Konrad 1 Reshetnyak, Yuriĭ Grigor’evich 1 Smirnov, Sergei Valer’evich 1 Sokolova, Vera 1 Sosinskiĭ, Alekseĭ Bronislavovich 1 Timorin, Vladlen Anatol’evich 1 Turaev, Vladimir Georgievich 1 Vasil’ev, Viktor Anatol’evich
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### Serials

 16 Russian Mathematical Surveys 4 Sibirskie Èlektronnye Matematicheskie Izvestiya 2 Functional Analysis and its Applications 2 Transactions of the Moscow Mathematical Society 2 Journal of Knot Theory and its Ramifications 2 St. Petersburg Mathematical Journal 2 Proceedings of the Steklov Institute of Mathematics 1 Mathematical Notes 1 Moscow University Mathematics Bulletin 1 Fundamenta Mathematicae 1 Geometriae Dedicata 1 Acta Applicandae Mathematicae 1 Algebra i Analiz 1 Journal of Mathematical Sciences (New York) 1 Sbornik: Mathematics 1 Journal of the European Mathematical Society (JEMS) 1 Moscow Mathematical Journal 1 Mathematical Surveys and Monographs 1 Panoramas et Synthèses 1 Journal of Modern Dynamics 1 Journal of Topology 1 Proceedings of the International Geometry Center 1 Electronic Geometry Model
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### Fields

 31 Manifolds and cell complexes (57-XX) 16 Dynamical systems and ergodic theory (37-XX) 10 Global analysis, analysis on manifolds (58-XX) 6 Group theory and generalizations (20-XX) 6 Optics, electromagnetic theory (78-XX) 4 Difference and functional equations (39-XX) 4 Quantum theory (81-XX) 3 Operator theory (47-XX) 2 General and overarching topics; collections (00-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Measure and integration (28-XX) 2 Partial differential equations (35-XX) 2 Geometry (51-XX) 2 Computer science (68-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Category theory; homological algebra (18-XX) 1 Functions of a complex variable (30-XX) 1 Integral transforms, operational calculus (44-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX)

### Citations contained in zbMATH Open

38 Publications have been cited 312 times in 221 Documents Cited by Year
Ordering braids. Zbl 1163.20024
Dehornoy, Patrick; Dynnikov, Ivan; Rolfsen, Dale; Wiest, Bert
2008
Arc-presentations of links: monotonic simplification. Zbl 1132.57006
Dynnikov, I. A.
2006
Discrete spectral symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds. Zbl 0928.35107
Novikov, S. P.; Dynnikov, I. A.
1997
Why are braids orderable? Zbl 1048.20021
Dehornoy, Patrick; Dynnikov, Ivan; Rolfsen, Dale; Wiest, Bert
2002
On the complexity of braids. Zbl 1187.20045
Dynnikov, Ivan; Wiest, Bert
2007
Geometry of the triangle equation on two-manifolds. Zbl 1046.39016
Dynnikov, I. A.; Novikov, S. P.
2003
Geometry of plane sections of the infinite regular skew polyhedron $$\{4, 6 | 4\}$$. Zbl 1165.28006
DeLeo, Roberto; Dynnikov, Ivan A.
2009
On a Yang-Baxter mapping and the Dehornoy ordering. Zbl 1067.20501
Dynnikov, I. A.
2002
Bypasses for rectangular diagrams. A proof of the Jones conjecture and related questions. Zbl 1307.57004
Dynnikov, I. A.; Prasolov, M. V.
2013
Topology of quasiperiodic functions on the plane. Zbl 1148.37043
Dynnikov, I. A.; Novikov, S. P.
2005
Semiclassical motion of the electron. A proof of the Novikov conjecture in general position and counterexamples. Zbl 0923.58043
Dynnikov, I. A.
1997
Integrable gradient flows and Morse theory. Zbl 0884.58022
Veselov, A. P.; Dynnikov, I. A.
1996
The geometry of the stability regions in Novikov’s problem on the semiclassical motion of an electron. Zbl 0935.57040
Dynnikov, I. A.
1999
Recognition algorithms in knot theory. Zbl 1063.57005
Dynnikov, I. A.
2003
Symmetric band complexes of thin type and chaotic sections which are not quite chaotic. Zbl 1335.57042
Dynnikov, Ivan; Skripchenko, Alexandra
2015
Interval identification systems and plane sections of 3-periodic surfaces. Zbl 1231.37024
Dynnikov, I. A.
2008
Proof of S. P. Novikov’s conjecture for the case of small perturbations of rational magnetic fields. Zbl 0778.58016
Dynnikov, I. A.
1992
Proof of S. P. Novikov’s conjecture on the semiclassical motion of an electron. Zbl 0808.58014
Dynnikov, I. A.
1993
Three-page representation of links. Zbl 0932.57010
Dynnikov, I. A.
1998
Three-page approach to knot theory. Encoding and local moves. Zbl 0947.57005
Dynnikov, I. A.
1999
Three-page approach to knot theory. Universal semigroup. Zbl 0958.57006
Dynnikov, I. A.
2000
On typical leaves of a measured foliated 2-complex of thin type. Zbl 1360.57029
Dynnikov, Ivan; Skripchenko, Alexandra
2014
A new way to represent links. One-dimensional formalism and untangling technology. Zbl 1006.57001
Dynnikov, I. A.
2001
Rectangular diagrams of surfaces: representability. Zbl 1378.57005
Dynnikov, Ivan A.; Prasolov, Maxim V.
2017
Exactly solvable cyclic Darboux $$q$$-chains. Zbl 1046.37043
Dynnikov, I. A.; Smirnov, S. V.
2002
Laplace transforms and simplicial connections. Zbl 0928.39009
Dynnikov, I. A.; Novikov, S. P.
1997
An example of a fractal set of plane directions having chaotic intersections with a fixed 3-periodic surface. Zbl 1149.28301
De Leo, R.; Dynnikov, I. A.
2007
A mathematical webservice for recognizing the unknot. Zbl 1011.68175
Andreeva, M. V.; Dynnikov, I. A.; Polthier, K.
2002
Conference “Dynamics in Siberia” dedicated to the 90th anniversary of B. V. Chirikov, Novosibirsk, Russia, February 26 – March 4, 2018. Abstracts. Zbl 1411.00034
Mironov, A. E.
2018
On equivalence of Legendrian knots. Zbl 1428.53092
Dynnikov, I. A.; Shastin, V. A.
2018
Surfaces in 3-torus: Geometry of plane sections. Zbl 0953.57001
Dynnikov, I.
1998
On independence of some pseudocharacters on braid groups. Zbl 1279.20045
Dynnikov, I. A.; Shastin, V. A.
2013
Intersections of level surfaces of pseudoperiodic functions. Zbl 0842.58017
Dynnikov, I. A.
1994
Classification of Legendrian knots of topological type $$7_6$$ with maximal Thurston-Bennequin number. Zbl 1436.57003
Dynnikov, Ivan; Prasolov, Maxim
2019
Dynnikov, Ivan A.
2019
On a new discretization of complex analysis. Zbl 1353.39004
Dynnikov, I. A.
2015
The conference “Dynamics in Siberia”, Novosibirsk, February 29–March 4, 2016. Zbl 1417.37037
Dynnikov, Ivan Alekseevich; Mironov, Andrey Evgenyevich; Taimanov, Iskander Asanovich; Vesnin, Andrey Yurievich
2016
Rectangular diagrams of surfaces: distinguishing Legendrian knots. Zbl 07433661
Dynnikov, Ivan; Prasolov, Maxim
2021
Rectangular diagrams of surfaces: distinguishing Legendrian knots. Zbl 07433661
Dynnikov, Ivan; Prasolov, Maxim
2021
Classification of Legendrian knots of topological type $$7_6$$ with maximal Thurston-Bennequin number. Zbl 1436.57003
Dynnikov, Ivan; Prasolov, Maxim
2019
Dynnikov, Ivan A.
2019
Conference “Dynamics in Siberia” dedicated to the 90th anniversary of B. V. Chirikov, Novosibirsk, Russia, February 26 – March 4, 2018. Abstracts. Zbl 1411.00034
Mironov, A. E.
2018
On equivalence of Legendrian knots. Zbl 1428.53092
Dynnikov, I. A.; Shastin, V. A.
2018
Rectangular diagrams of surfaces: representability. Zbl 1378.57005
Dynnikov, Ivan A.; Prasolov, Maxim V.
2017
The conference “Dynamics in Siberia”, Novosibirsk, February 29–March 4, 2016. Zbl 1417.37037
Dynnikov, Ivan Alekseevich; Mironov, Andrey Evgenyevich; Taimanov, Iskander Asanovich; Vesnin, Andrey Yurievich
2016
Symmetric band complexes of thin type and chaotic sections which are not quite chaotic. Zbl 1335.57042
Dynnikov, Ivan; Skripchenko, Alexandra
2015
On a new discretization of complex analysis. Zbl 1353.39004
Dynnikov, I. A.
2015
On typical leaves of a measured foliated 2-complex of thin type. Zbl 1360.57029
Dynnikov, Ivan; Skripchenko, Alexandra
2014
Bypasses for rectangular diagrams. A proof of the Jones conjecture and related questions. Zbl 1307.57004
Dynnikov, I. A.; Prasolov, M. V.
2013
On independence of some pseudocharacters on braid groups. Zbl 1279.20045
Dynnikov, I. A.; Shastin, V. A.
2013
Geometry of plane sections of the infinite regular skew polyhedron $$\{4, 6 | 4\}$$. Zbl 1165.28006
DeLeo, Roberto; Dynnikov, Ivan A.
2009
Ordering braids. Zbl 1163.20024
Dehornoy, Patrick; Dynnikov, Ivan; Rolfsen, Dale; Wiest, Bert
2008
Interval identification systems and plane sections of 3-periodic surfaces. Zbl 1231.37024
Dynnikov, I. A.
2008
On the complexity of braids. Zbl 1187.20045
Dynnikov, Ivan; Wiest, Bert
2007
An example of a fractal set of plane directions having chaotic intersections with a fixed 3-periodic surface. Zbl 1149.28301
De Leo, R.; Dynnikov, I. A.
2007
Arc-presentations of links: monotonic simplification. Zbl 1132.57006
Dynnikov, I. A.
2006
Topology of quasiperiodic functions on the plane. Zbl 1148.37043
Dynnikov, I. A.; Novikov, S. P.
2005
Geometry of the triangle equation on two-manifolds. Zbl 1046.39016
Dynnikov, I. A.; Novikov, S. P.
2003
Recognition algorithms in knot theory. Zbl 1063.57005
Dynnikov, I. A.
2003
Why are braids orderable? Zbl 1048.20021
Dehornoy, Patrick; Dynnikov, Ivan; Rolfsen, Dale; Wiest, Bert
2002
On a Yang-Baxter mapping and the Dehornoy ordering. Zbl 1067.20501
Dynnikov, I. A.
2002
Exactly solvable cyclic Darboux $$q$$-chains. Zbl 1046.37043
Dynnikov, I. A.; Smirnov, S. V.
2002
A mathematical webservice for recognizing the unknot. Zbl 1011.68175
Andreeva, M. V.; Dynnikov, I. A.; Polthier, K.
2002
A new way to represent links. One-dimensional formalism and untangling technology. Zbl 1006.57001
Dynnikov, I. A.
2001
Three-page approach to knot theory. Universal semigroup. Zbl 0958.57006
Dynnikov, I. A.
2000
The geometry of the stability regions in Novikov’s problem on the semiclassical motion of an electron. Zbl 0935.57040
Dynnikov, I. A.
1999
Three-page approach to knot theory. Encoding and local moves. Zbl 0947.57005
Dynnikov, I. A.
1999
Three-page representation of links. Zbl 0932.57010
Dynnikov, I. A.
1998
Surfaces in 3-torus: Geometry of plane sections. Zbl 0953.57001
Dynnikov, I.
1998
Discrete spectral symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds. Zbl 0928.35107
Novikov, S. P.; Dynnikov, I. A.
1997
Semiclassical motion of the electron. A proof of the Novikov conjecture in general position and counterexamples. Zbl 0923.58043
Dynnikov, I. A.
1997
Laplace transforms and simplicial connections. Zbl 0928.39009
Dynnikov, I. A.; Novikov, S. P.
1997
Integrable gradient flows and Morse theory. Zbl 0884.58022
Veselov, A. P.; Dynnikov, I. A.
1996
Intersections of level surfaces of pseudoperiodic functions. Zbl 0842.58017
Dynnikov, I. A.
1994
Proof of S. P. Novikov’s conjecture on the semiclassical motion of an electron. Zbl 0808.58014
Dynnikov, I. A.
1993
Proof of S. P. Novikov’s conjecture for the case of small perturbations of rational magnetic fields. Zbl 0778.58016
Dynnikov, I. A.
1992
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### Cited by 270 Authors

 16 Dynnikov, Ivan Alekseevich 8 Dehornoy, Patrick 7 Ito, Tetsuya 6 Yurttaş, Saadet Öykü 5 Bobenko, Alexander Ivanovich 5 Clay, Adam 5 De Leo, Roberto 4 Lee, Hwa Jeong 4 Mal’tsev, Andreĭ Yakovlevich 4 Navas, Andrés 4 Novikov, Sergeĭ Petrovich 4 Prasolov, Maxim V. 4 Rivas, Cristóbal 4 Skripchenko, Alexandra 3 Fromentin, Jean 3 Hall, Toby 3 Hayashi, Chuichiro 3 Macias-Virgós, Enrique 3 Ozsváth, Peter Steven 3 Paris, Luis 3 Santini, Paolo Maria 3 Shemyakova, Ekaterina 3 Szabo, Zoltan 2 Adler, Vsevolod Eduardovich 2 Ando, Tatsuo 2 Birman, Joan S. 2 Doliwa, Adam 2 Fish, Andrew 2 Grinevich, Pëtr Georgievich 2 Günther, Felix 2 Khabibullin, Ismagil Talgatovich 2 Halava, Vesa 2 Harju, Tero 2 Hubert, Pascal 2 Jugé, Vincent 2 Kawamuro, Keiko 2 Kim, Seongjeong 2 Koberda, Thomas 2 Kurlin, Vitaliy 2 Lisitsa, Alexei 2 Manolescu, Ciprian 2 Manturov, Vassiliĭ Olegovich 2 Menasco, William W. 2 Nieszporski, Maciej 2 Niskanen, Reino 2 Pereira-Sáez, María José 2 Potapov, Igor 2 Skopenkov, Mikhail B. 2 Thurston, Dylan Paul 2 Wehrung, Friedrich 2 Wiest, Bertold 1 Aceves, Elaina 1 An, Byung Hee 1 Antonevich, Anatolij Borisovich 1 Arcis, Diego 1 Arnoux, Pierre 1 Audoux, Benjamin 1 Avila Cordeiro de Melo, Artur 1 Baldridge, Scott Jeremy 1 Baldwin, John A. 1 Beliakova, Anna 1 Bell, Mark Christopher 1 Belousov, Yu. S. 1 ben Simon, Gabi 1 Bergeron, Nicolas 1 Bessis, David 1 Birindelli, Isabeau 1 Bohle, Christoph 1 Bücking, Ulrike 1 Budišić, Marko 1 Burton, Benjamin A. 1 Camilo, Giancarlo 1 Campos, Hugo M. 1 Cassaigne, Julien 1 Castillo Pérez, Raúl 1 Cattabriga, Alessia 1 Chakrabarti, Raj 1 Chelkak, Dmitry 1 Chernavskiĭ, Alekseĭ Viktorovich 1 Chernavskikh, M. M. 1 Chouraqui, Fabienne 1 Chow, Bennett 1 Chterental, Oleg 1 Cimasoni, David 1 Colton, Leslie 1 Conner, Gregory R. 1 Corson, Samuel M. 1 Crisp, John D. C. 1 Cumplido, María 1 Dabkowska, Malgorzata A. 1 Dabkowski, Mieczysław K. 1 D’Ambra, Giuseppina 1 De Lima, Juliana Roberta Theodoro 1 de Mattos, Denise 1 Deloup, Florian L. 1 Diao, Yuanan 1 Droz, Jean-Marie 1 Dujmović, Vida 1 Dunn, Sierra 1 Egorov, Dima V. ...and 170 more Authors
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### Cited in 96 Serials

 32 Journal of Knot Theory and its Ramifications 11 Algebraic & Geometric Topology 8 Proceedings of the Steklov Institute of Mathematics 7 St. Petersburg Mathematical Journal 6 Geometry & Topology 5 Advances in Mathematics 5 Journal of Algebra 4 Journal of Mathematical Physics 4 Theoretical and Mathematical Physics 4 Proceedings of the American Mathematical Society 4 Discrete & Computational Geometry 4 Groups, Geometry, and Dynamics 3 Mathematical Notes 3 Functional Analysis and its Applications 3 Semigroup Forum 3 Siberian Mathematical Journal 3 Transactions of the Moscow Mathematical Society 3 Topology and its Applications 3 International Journal of Algebra and Computation 2 Russian Mathematical Surveys 2 Annales de l’Institut Fourier 2 Duke Mathematical Journal 2 Geometriae Dedicata 2 Journal für die Reine und Angewandte Mathematik 2 Monatshefte für Mathematik 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Transactions of the American Mathematical Society 2 Acta Applicandae Mathematicae 2 Annals of Pure and Applied Logic 2 Annals of Global Analysis and Geometry 2 Differential Geometry and its Applications 2 Bulletin of the American Mathematical Society. New Series 2 Journal of Mathematical Sciences (New York) 2 Annales Mathématiques Blaise Pascal 2 Doklady Mathematics 2 Annals of Mathematics. Second Series 2 Journal of the European Mathematical Society (JEMS) 2 Communications in Contemporary Mathematics 2 Sibirskie Èlektronnye Matematicheskie Izvestiya 1 Bulletin of the Australian Mathematical Society 1 Communications in Algebra 1 Discrete Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Journal of Statistical Physics 1 Letters in Mathematical Physics 1 Nuclear Physics. B 1 Canadian Mathematical Bulletin 1 Illinois Journal of Mathematics 1 Inventiones Mathematicae 1 Journal of Combinatorial Theory. Series A 1 Journal of the Mathematical Society of Japan 1 Journal of Optimization Theory and Applications 1 Journal of Pure and Applied Algebra 1 Manuscripta Mathematica 1 Mathematische Annalen 1 Mathematische Zeitschrift 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Osaka Journal of Mathematics 1 Theoretical Computer Science 1 Tohoku Mathematical Journal. Second Series 1 Ergodic Theory and Dynamical Systems 1 Acta Mathematica Hungarica 1 Physica D 1 Information and Computation 1 Journal of the Ramanujan Mathematical Society 1 Sugaku Expositions 1 Geometric and Functional Analysis. GAFA 1 Archive for Mathematical Logic 1 Applicable Algebra in Engineering, Communication and Computing 1 Journal of Nonlinear Science 1 Experimental Mathematics 1 Journal of Algebraic Combinatorics 1 Russian Journal of Mathematical Physics 1 Turkish Journal of Mathematics 1 The New York Journal of Mathematics 1 Selecta Mathematica. New Series 1 Discrete and Continuous Dynamical Systems 1 Mathematical Physics, Analysis and Geometry 1 Chicago Journal of Theoretical Computer Science 1 Chaos 1 Journal of High Energy Physics 1 Lobachevskii Journal of Mathematics 1 Journal of Nonlinear Mathematical Physics 1 SIAM Journal on Applied Dynamical Systems 1 Central European Journal of Mathematics 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Complex Variables and Elliptic Equations 1 Functional Analysis and Other Mathematics 1 Journal of Fixed Point Theory and Applications 1 Journal of Modern Dynamics 1 Journal of Topology and Analysis 1 Ufimskiĭ Matematicheskiĭ Zhurnal 1 Kyoto Journal of Mathematics 1 Proceedings of the International Geometry Center 1 Bulletin of Mathematical Sciences
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### Cited in 45 Fields

 122 Manifolds and cell complexes (57-XX) 73 Group theory and generalizations (20-XX) 48 Dynamical systems and ergodic theory (37-XX) 20 Order, lattices, ordered algebraic structures (06-XX) 15 Differential geometry (53-XX) 14 Global analysis, analysis on manifolds (58-XX) 14 Computer science (68-XX) 10 Difference and functional equations (39-XX) 10 Convex and discrete geometry (52-XX) 10 Quantum theory (81-XX) 9 Functions of a complex variable (30-XX) 9 Partial differential equations (35-XX) 8 Combinatorics (05-XX) 7 Algebraic topology (55-XX) 6 Mathematical logic and foundations (03-XX) 6 Associative rings and algebras (16-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Topological groups, Lie groups (22-XX) 4 Measure and integration (28-XX) 4 Potential theory (31-XX) 4 Mechanics of particles and systems (70-XX) 4 Optics, electromagnetic theory (78-XX) 3 General and overarching topics; collections (00-XX) 3 Category theory; homological algebra (18-XX) 3 Ordinary differential equations (34-XX) 3 General topology (54-XX) 3 Numerical analysis (65-XX) 2 General algebraic systems (08-XX) 2 Algebraic geometry (14-XX) 2 Operator theory (47-XX) 2 Geometry (51-XX) 2 Probability theory and stochastic processes (60-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Number theory (11-XX) 1 Commutative algebra (13-XX) 1 Nonassociative rings and algebras (17-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Fluid mechanics (76-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX)