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Lazutkin, Vladimir Fedorovich

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Author ID: lazutkin.vladimir-fedorovich Recent zbMATH articles by "Lazutkin, Vladimir Fedorovich"
Published as: Lazutkin, V. F.; Lazutkin, Vladimir F.; Lazutkin, V.
External Links: MGP · Math-Net.Ru · GND
Documents Indexed: 62 Publications since 1965, including 2 Books
1 Contribution as Editor
Biographic References: 2 Publications
Co-Authors: 14 Co-Authors with 22 Joint Publications
309 Co-Co-Authors
all top 5

Serials

4 Functional Analysis and its Applications
4 Soviet Mathematics. Doklady
3 Vestnik Leningradskogo Universiteta. Matematika, Mekhanika, Astronomiya
3 Problemy Matematicheskoĭ Fiziki
2 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki
2 Funktsional’nyĭ Analiz i ego Prilozheniya
2 Journal of Soviet Mathematics
2 Mathematics of the USSR. Izvestiya
2 Physica D
2 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya
2 U.S.S.R. Computational Mathematics and Mathematical Physics
2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
2 Regularnaya & Khaoticheskaya Dinamika
2 Regular and Chaotic Dynamics
2 Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta Imeni V. A. Steklova
1 Communications in Mathematical Physics
1 Mathematical Notes
1 Physics Letters. A
1 Russian Mathematical Surveys
1 Uspekhi Matematicheskikh Nauk [N. S.]
1 Chaos, Solitons and Fractals
1 Algebra i Analiz
1 Leningrad Mathematical Journal
1 Vestnik Leningrad University. Mathematics
1 Journal of Mathematical Sciences (New York)
1 St. Petersburg Mathematical Journal
1 Chaos
1 Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge
1 Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Fundamental’nye Napravleniya
1 Proceedings of the Steklov Institute of Mathematics
1 Trudy Matematicheskogo Instituta Imeni V. A. Steklova
1 Translations. Series 2. American Mathematical Society
1 Progress in Nonlinear Differential Equations and Their Applications

Publications by Year

Citations contained in zbMATH Open

39 Publications have been cited 334 times in 264 Documents Cited by Year
The existence of caustics for a billiard problem in a convex domain. Zbl 0277.52002
Lazutkin, V. F.
51
1974
KAM theory and semiclassical approximations to eigenfunctions. With an addendum by A. I. Shnirelman. Zbl 0814.58001
Lazutkin, Vladimir F.
49
1993
Splitting of separatrices for standard and semistandard mappings. Zbl 0825.58033
Lazutkin, V. F.; Schachmannski, I. G.; Tabanov, M. B.
31
1989
Die Existenz von Kaustiken für das Billardproblem in einem konvexen Gebiet. Zbl 0256.52001
Lazutkin, V. F.
26
1973
Splitting of separatrices: Perturbation theory and exponential smallness. Zbl 1071.37039
Gel’freich, V. G.; Lazutkin, V. F.
21
2001
Exponentially small splittings in Hamiltonian systems. Zbl 0899.58016
Gelfreich, V. G.; Lazutkin, V. F.; Tabanov, M. B.
20
1991
Normal forms and versal deformations for Hill’s equation. Zbl 0357.34021
Lazutkin, V. F.; Pankratova, T. F.
17
1976
Splitting of separatrices for the Chirikov standard map. Zbl 1120.37039
Lazutkin, V. F.
16
2005
A refined formula for the separatrix splitting for the standard map. Zbl 0812.70017
Gelfreich, V. G.; Lazutkin, V. F.; Svanidze, N. V.
16
1994
Convex billiards and eigenfunctions of the Laplace operator. (Vypuklyj billiard i sobstvennye funktsii operatora Laplasa). Zbl 0532.58031
Lazutkin, V. F.
15
1981
Some remarks on the problem of ergodicity of the standard map. Zbl 1115.37330
Giorgilli, A.; Lazutkin, V. F.
6
2000
On the width of the instability zone near the separatrices of a standard mapping. Zbl 0733.58038
Lazutkin, V. F.
6
1991
Asymptotics of the width of gaps in the spectrum of the Sturm-Liouville operator with a periodic potential. Zbl 0318.34035
Lazutkin, V. F.; Pankratova, T. F.
6
1974
On the asymptotics of the eigenfunctions of the Laplacian. Zbl 0232.35075
Lazutkin, V. F.
5
1971
Quasi-classical asymptotics of eigenfunctions. Zbl 0657.35098
Lazutkin, V. F.
4
1988
Asymptotics of the eigenvalues of the Laplacian and quasimodes. A series of quasimodes corresponding to a system of caustics close to the boundary of the domain. Zbl 0282.35063
Lazutkin, V. F.
4
1974
The existence of an infinite number of elliptic and hyperbolic periodic trajectories for a convex billiard. Zbl 0298.58006
Dvorin, M. M.; Lazutkin, V. F.
4
1973
Percival variational principle for invariant measures and commensurate- incommensurate phase transitions in one-dimensional chains. Zbl 0564.58015
Lazutkin, V. F.; Terman, D. Ya.
3
1984
Estimation of the remainder in the Weyl formula. Zbl 0483.35065
Lazutkin, V. F.; Terman, D. Ya.
3
1982
Analytic integrals of the semistandard map, and splitting of separatrices. Zbl 0725.58028
Lazutkin, V. F.
3
1990
Construction of an asymptotic series of eigenfunctions of the ’bouncing ball’ type. Zbl 0211.13802
Lazutkin, V. F.
3
1968
Semiclassical asymptotics of eigenfunctions. Zbl 0907.35093
Lazutkin, V. F.
2
1988
Visualization of a hyperbolic structure in area preserving maps. Zbl 0922.58059
Giorgilli, A.; Lazutkin, V. F.; Simó, C.
2
1997
Number of quasimodes of ”bouncing-ball” type. Zbl 0532.35057
Lazutkin, V. F.; Terman, D. Ya.
2
1984
Signature of invertible symmetric matrices. Zbl 0738.15004
Lazutkin, V. F.
2
1988
Splitting of complex separatrices. Zbl 0667.58051
Lazutkin, V. F.
2
1988
Making fractals fat. Zbl 1076.37506
Lazutkin, V. F.
2
1999
Die Existenz eines Kontinuums geschlossener invarianter Kurven für ein konvexes Billiard. Zbl 0237.58014
Lazutkin, V. F.
2
1972
Resurgent approach to the separatrices splitting. Zbl 0938.37524
Lazutkin, Vladimir F.
1
1993
Seminar on dynamical systems. Euler International Mathematical Institut, St. Petersburg, Russia, October 14-25 and November 18-29, 1991. Zbl 0782.00078
1
1994
The splitting of separatrices for a standard family of area-preserving transformations. Zbl 0797.58064
Lazutkin, V. F.
1
1993
Homoclinic orbits in the complex domain. Zbl 0886.58047
Lazutkin, V. F.; Simó, C.
1
1997
Complex billiard. Zbl 0606.35018
Lazutkin, V. F.
1
1986
An analytic integral along the separatrix of the semistandard map: Existence and an exponential estimate for the distance between the stable and unstable separatrices. Zbl 0791.58036
Lazutkin, V. F.
1
1992
An analytic integral along the separatrix of the semistandard map: Existence and an exponential estimate for the distance between the stable and unstable separatrices. Zbl 0768.58017
Lazutkin, V. F.
1
1992
Complexified quantum rules. Zbl 0909.58016
Lazutkin, V. F.; Terman, D. Ya.
1
1993
An estimate of the length of the gaps in the spectrum of the Laplace operator for a plane convex domain. Zbl 0425.35074
Lazutkin, V. F.
1
1979
Über Eigenfunktionen, die in der Nähe einer abgeschlossenen Geodätischen konzentriert sind. Zbl 0164.13601
Babich, V. M.; Lazutkin, V. F.
1
1967
The asymptotics of the eigenfunctions of the Laplace operator, concentrated near the boundary of a region. Zbl 0183.18302
Lazutkin, V. F.
1
1967
Splitting of separatrices for the Chirikov standard map. Zbl 1120.37039
Lazutkin, V. F.
16
2005
Splitting of separatrices: Perturbation theory and exponential smallness. Zbl 1071.37039
Gel’freich, V. G.; Lazutkin, V. F.
21
2001
Some remarks on the problem of ergodicity of the standard map. Zbl 1115.37330
Giorgilli, A.; Lazutkin, V. F.
6
2000
Making fractals fat. Zbl 1076.37506
Lazutkin, V. F.
2
1999
Visualization of a hyperbolic structure in area preserving maps. Zbl 0922.58059
Giorgilli, A.; Lazutkin, V. F.; Simó, C.
2
1997
Homoclinic orbits in the complex domain. Zbl 0886.58047
Lazutkin, V. F.; Simó, C.
1
1997
A refined formula for the separatrix splitting for the standard map. Zbl 0812.70017
Gelfreich, V. G.; Lazutkin, V. F.; Svanidze, N. V.
16
1994
Seminar on dynamical systems. Euler International Mathematical Institut, St. Petersburg, Russia, October 14-25 and November 18-29, 1991. Zbl 0782.00078
1
1994
KAM theory and semiclassical approximations to eigenfunctions. With an addendum by A. I. Shnirelman. Zbl 0814.58001
Lazutkin, Vladimir F.
49
1993
Resurgent approach to the separatrices splitting. Zbl 0938.37524
Lazutkin, Vladimir F.
1
1993
The splitting of separatrices for a standard family of area-preserving transformations. Zbl 0797.58064
Lazutkin, V. F.
1
1993
Complexified quantum rules. Zbl 0909.58016
Lazutkin, V. F.; Terman, D. Ya.
1
1993
An analytic integral along the separatrix of the semistandard map: Existence and an exponential estimate for the distance between the stable and unstable separatrices. Zbl 0791.58036
Lazutkin, V. F.
1
1992
An analytic integral along the separatrix of the semistandard map: Existence and an exponential estimate for the distance between the stable and unstable separatrices. Zbl 0768.58017
Lazutkin, V. F.
1
1992
Exponentially small splittings in Hamiltonian systems. Zbl 0899.58016
Gelfreich, V. G.; Lazutkin, V. F.; Tabanov, M. B.
20
1991
On the width of the instability zone near the separatrices of a standard mapping. Zbl 0733.58038
Lazutkin, V. F.
6
1991
Analytic integrals of the semistandard map, and splitting of separatrices. Zbl 0725.58028
Lazutkin, V. F.
3
1990
Splitting of separatrices for standard and semistandard mappings. Zbl 0825.58033
Lazutkin, V. F.; Schachmannski, I. G.; Tabanov, M. B.
31
1989
Quasi-classical asymptotics of eigenfunctions. Zbl 0657.35098
Lazutkin, V. F.
4
1988
Semiclassical asymptotics of eigenfunctions. Zbl 0907.35093
Lazutkin, V. F.
2
1988
Signature of invertible symmetric matrices. Zbl 0738.15004
Lazutkin, V. F.
2
1988
Splitting of complex separatrices. Zbl 0667.58051
Lazutkin, V. F.
2
1988
Complex billiard. Zbl 0606.35018
Lazutkin, V. F.
1
1986
Percival variational principle for invariant measures and commensurate- incommensurate phase transitions in one-dimensional chains. Zbl 0564.58015
Lazutkin, V. F.; Terman, D. Ya.
3
1984
Number of quasimodes of ”bouncing-ball” type. Zbl 0532.35057
Lazutkin, V. F.; Terman, D. Ya.
2
1984
Estimation of the remainder in the Weyl formula. Zbl 0483.35065
Lazutkin, V. F.; Terman, D. Ya.
3
1982
Convex billiards and eigenfunctions of the Laplace operator. (Vypuklyj billiard i sobstvennye funktsii operatora Laplasa). Zbl 0532.58031
Lazutkin, V. F.
15
1981
An estimate of the length of the gaps in the spectrum of the Laplace operator for a plane convex domain. Zbl 0425.35074
Lazutkin, V. F.
1
1979
Normal forms and versal deformations for Hill’s equation. Zbl 0357.34021
Lazutkin, V. F.; Pankratova, T. F.
17
1976
The existence of caustics for a billiard problem in a convex domain. Zbl 0277.52002
Lazutkin, V. F.
51
1974
Asymptotics of the width of gaps in the spectrum of the Sturm-Liouville operator with a periodic potential. Zbl 0318.34035
Lazutkin, V. F.; Pankratova, T. F.
6
1974
Asymptotics of the eigenvalues of the Laplacian and quasimodes. A series of quasimodes corresponding to a system of caustics close to the boundary of the domain. Zbl 0282.35063
Lazutkin, V. F.
4
1974
Die Existenz von Kaustiken für das Billardproblem in einem konvexen Gebiet. Zbl 0256.52001
Lazutkin, V. F.
26
1973
The existence of an infinite number of elliptic and hyperbolic periodic trajectories for a convex billiard. Zbl 0298.58006
Dvorin, M. M.; Lazutkin, V. F.
4
1973
Die Existenz eines Kontinuums geschlossener invarianter Kurven für ein konvexes Billiard. Zbl 0237.58014
Lazutkin, V. F.
2
1972
On the asymptotics of the eigenfunctions of the Laplacian. Zbl 0232.35075
Lazutkin, V. F.
5
1971
Construction of an asymptotic series of eigenfunctions of the ’bouncing ball’ type. Zbl 0211.13802
Lazutkin, V. F.
3
1968
Über Eigenfunktionen, die in der Nähe einer abgeschlossenen Geodätischen konzentriert sind. Zbl 0164.13601
Babich, V. M.; Lazutkin, V. F.
1
1967
The asymptotics of the eigenfunctions of the Laplace operator, concentrated near the boundary of a region. Zbl 0183.18302
Lazutkin, V. F.
1
1967
all top 5

Cited by 288 Authors

12 Gelfreich, Vassili
9 Bunimovich, Leonid Abramovich
8 Kaloshin, Vadim Yu.
6 Lazutkin, Vladimir Fedorovich
6 Ramírez-Ros, Rafael
5 Delshams, Amadeu
5 Dobrokhotov, Sergei Yurievich
5 Sardanashvily, Gennadi A.
5 Simó, Carles
5 Sorrentino, Alfonso
4 Anikin, A. Yu.
4 Giachetta, Giovanni
4 Oblak, Blagoje
4 Popov, Georgi St.
4 M-Seara, Tere
3 Amiran, Edoh Y.
3 Bialy, Misha
3 Damjanović, Danijela
3 de Simoi, Jacopo
3 Fontich, Ernest
3 Gutiérrez, Pere
3 Gutkin, Eugene
3 Katok, Anatole
3 Lerman, Lev
3 MacKay, Robert Sinclair
3 Mangiarotti, Luigi
3 Markarian, Roberto
3 Mironov, Andreĭ Evgen’evich
3 Nazaikinskii, Vladimir E.
3 Neĭshtadt, Anatoliĭ Iserovich
3 Sinaĭ, Yakov Grigor’evich
3 Tabachnikov, Serge L.
3 Terman, D. Ya.
3 Treshchev, Dmitriĭ Valer’evich
3 Tsvetkova, Anna V.
3 Zanelli, Lorenzo
2 Ablowitz, Mark Jay
2 Amick, Charles J.
2 Baldomá, Inmaculada
2 Broer, Henk W.
2 Cardin, Franco
2 Chernov, Nikolai Ivanovich
2 Chernyshev, G. N.
2 Ching, Emily S. C.
2 Cincotta, Pablo M.
2 Colin de Verdière, Yves
2 Donnay, Victor J.
2 Florentin, Dan Itzhak
2 Fomenko, Anatoliĭ Timofeevich
2 Fruchard, Augustin
2 Galkowski, Jeffrey
2 Gasiorek, Sean
2 Glutsyuk, Alexey A.
2 Gonchenko, Marina S.
2 Gruber, Peter Manfred
2 Guardia, Marcel
2 Guha, Partha
2 Guieu, Laurent
2 Guo, Jingwei
2 Guzzo, Massimiliano
2 Han, Ray P. S.
2 Kadanoff, Leo Philip
2 Knill, Oliver
2 Kovachev, Valery
2 Kuksin, Sergeĭ B.
2 Luo, Albert C. J.
2 Martínez, Regina
2 Ostrover, Yaron
2 Petkov, Vesselin M.
2 Petković, Boris
2 Pinto de Carvalho, Sônia
2 Rom-Kedar, Vered
2 Rosen, Daniel
2 Sarnak, Peter Clive
2 Sellama, Hocine
2 Sevryuk, Mikhail Borisovich
2 Stefanov, Plamen D.
2 Stoyanov, Luchezar N.
2 Turaev, Dmitry V.
2 Vedyushkina, Viktoriya Viktorovna
2 Wang, Weiwei
2 Wang, Zhenqi Jenny
2 Wang, Zuoqin
2 Wojtkowski, Maciej P.
2 Zaslavskiĭ, Georgiĭ Moiseevich
2 Zhang, Hongkun
2 Zhang, Pengfei
1 Ahn, Taehoon
1 Albers, Peter
1 Alfimov, Georgiĭ Leonidovich
1 Arnaiz, Víctor
1 Arslan, İlker
1 Artstein-Avidan, Shiri
1 Avila Cordeiro de Melo, Artur
1 Bailey, David Harold
1 Bartuccelli, Michele V.
1 Batal, Ahmet
1 Berger, Marcel
1 Berger, Pierre
1 Berglund, Nils
...and 188 more Authors
all top 5

Cited in 95 Serials

23 Communications in Mathematical Physics
17 Physica D
17 Chaos
15 Regular and Chaotic Dynamics
7 Chaos, Solitons and Fractals
6 Journal of Geometry and Physics
6 Journal of Soviet Mathematics
6 Ergodic Theory and Dynamical Systems
6 Journal of Mathematical Sciences (New York)
5 Journal of Mathematical Physics
5 Journal of Statistical Physics
5 Nonlinearity
5 Physics Letters. A
5 Advances in Mathematics
5 Bulletin of the American Mathematical Society. New Series
5 Journal of High Energy Physics
4 Journal of Applied Mathematics and Mechanics
4 Mathematical Notes
4 Annales de l’Institut Fourier
4 Duke Mathematical Journal
4 Functional Analysis and its Applications
4 Mathematische Zeitschrift
4 Journal of Nonlinear Science
4 Annals of Mathematics. Second Series
3 Israel Journal of Mathematics
3 Theoretical and Mathematical Physics
3 Journal of Differential Equations
3 Transactions of the American Mathematical Society
3 Celestial Mechanics and Dynamical Astronomy
3 Electronic Research Announcements of the American Mathematical Society
3 Discrete and Continuous Dynamical Systems
2 Journal of Mathematical Analysis and Applications
2 Russian Mathematical Surveys
2 Ukrainian Mathematical Journal
2 Journal of Functional Analysis
2 Proceedings of the American Mathematical Society
2 Annales de l’Institut Henri Poincaré. Physique Théorique
2 Experimental Mathematics
2 Journal of Dynamical and Control Systems
1 Computers & Mathematics with Applications
1 Journal of Computational Physics
1 Physica A
1 Wave Motion
1 Reviews in Mathematical Physics
1 Applied Mathematics and Computation
1 Archiv der Mathematik
1 Bulletin de la Société Mathématique de France
1 Commentarii Mathematici Helvetici
1 Inventiones Mathematicae
1 Journal of Geometry
1 Mathematische Annalen
1 Memoirs of the American Mathematical Society
1 Quaestiones Mathematicae
1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
1 Asymptotic Analysis
1 The Journal of Geometric Analysis
1 Geometric and Functional Analysis. GAFA
1 Computational Mathematics and Mathematical Physics
1 Celestial Mechanics
1 Journal de Mathématiques Pures et Appliquées. Neuvième Série
1 Linear Algebra and its Applications
1 Proceedings of the National Academy of Sciences of the United States of America
1 SIAM Journal on Mathematical Analysis
1 Journal of Dynamics and Differential Equations
1 Boletim da Sociedade Brasileira de Matemática. Nova Série
1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
1 Continuum Mechanics and Thermodynamics
1 Potential Analysis
1 Russian Journal of Mathematical Physics
1 St. Petersburg Mathematical Journal
1 Annales Mathématiques Blaise Pascal
1 NoDEA. Nonlinear Differential Equations and Applications
1 Journal of Difference Equations and Applications
1 The Journal of Fourier Analysis and Applications
1 Mathematical Physics, Analysis and Geometry
1 Journal for Geometry and Graphics
1 Infinite Dimensional Analysis, Quantum Probability and Related Topics
1 Journal of Mathematical Fluid Mechanics
1 Journal of the European Mathematical Society (JEMS)
1 Qualitative Theory of Dynamical Systems
1 International Journal of Nonlinear Sciences and Numerical Simulation
1 Differential Equations
1 Nihonkai Mathematical Journal
1 Dynamical Systems
1 Advances in Complex Systems
1 Proceedings of the Steklov Institute of Mathematics
1 Journal of Fixed Point Theory and Applications
1 Journal of Modern Dynamics
1 Nonlinear Analysis. Hybrid Systems
1 Journal of Spectral Theory
1 Annales Mathématiques du Québec
1 Nonlinear Analysis. Theory, Methods & Applications
1 Journal de l’École Polytechnique – Mathématiques
1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
1 Annales Henri Lebesgue
all top 5

Cited in 39 Fields

182 Dynamical systems and ergodic theory (37-XX)
53 Mechanics of particles and systems (70-XX)
45 Partial differential equations (35-XX)
35 Ordinary differential equations (34-XX)
32 Global analysis, analysis on manifolds (58-XX)
29 Quantum theory (81-XX)
24 Differential geometry (53-XX)
11 Statistical mechanics, structure of matter (82-XX)
10 Difference and functional equations (39-XX)
9 Numerical analysis (65-XX)
8 Mechanics of deformable solids (74-XX)
7 Convex and discrete geometry (52-XX)
7 Relativity and gravitational theory (83-XX)
6 Operator theory (47-XX)
5 Nonassociative rings and algebras (17-XX)
5 Topological groups, Lie groups (22-XX)
5 Special functions (33-XX)
4 Number theory (11-XX)
4 Measure and integration (28-XX)
4 Optics, electromagnetic theory (78-XX)
3 Linear and multilinear algebra; matrix theory (15-XX)
3 Functional analysis (46-XX)
2 Algebraic geometry (14-XX)
2 Functions of a complex variable (30-XX)
2 Geometry (51-XX)
2 Fluid mechanics (76-XX)
1 General and overarching topics; collections (00-XX)
1 History and biography (01-XX)
1 Combinatorics (05-XX)
1 Category theory; homological algebra (18-XX)
1 Group theory and generalizations (20-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Integral transforms, operational calculus (44-XX)
1 Integral equations (45-XX)
1 Calculus of variations and optimal control; optimization (49-XX)
1 General topology (54-XX)
1 Manifolds and cell complexes (57-XX)
1 Computer science (68-XX)
1 Information and communication theory, circuits (94-XX)

Citations by Year