List of publications by V. F. Lazutkin

Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 13-22

Bibliographie

[1] “Expansion in Terms of Functions Connected with Watson Transform”, Third All-Union Symposium of Wave Diffraction, Abstracts of Papers, M., 1964, 45–47

[2] “Parabolic Equation and Asymptotics of Eigenfunctions of Helmholtz equation for 3-dimensional Domains”, Vestn. LGU, Ser. Phys. and Chem., 1965, no. 22, 52–57 | Zbl

[3] “Expansion in Terms of Eigenfunctions of Nonselfajoint Operator Connected with Watson Transform”, Vestn. LGU, Ser. Mat., Mech., and Astr., 1966, no. 1, 38–50 | Zbl

[4] “Asymptotics of the Laplacian's Eigenfunctions Concentrated Near a Boundary of the Domain”, J. of Comput. Math. and Math. Phys., 7:6 (1967), 1237–1249 | MR

[5] “Eigenfunctions Concentrated Near a Closed Geodesic”, Probl. Math. Phys. LGU, 1967, no. 2, 15–25 (with V. M. Babich) | Zbl

[6] “Eigenfunctions Concentrated Near a Closed Geodesic”, 4th All-Union Symposium of Wave Propagation and Diffraction, Abstracts of Papers, Kharkov, 1967 (with V. M. Babich)

[7] “Construction of Asymptotic Series for Eigenfunctions of “Bouncing Ball” Type”, 4th All-Union Symposium of Wave Propagation and Diffraction, Abstracts of Papers, Kharkov, 1967

[8] Asymptotic Expansions for Laplacian's Eigenfunctions Concentrated Near Some One-dimensional Cycles, LOMI AN SSSR, Manuscript of Thesis, 1967

[9] “Construction of Asymptotic Series for Eigenfunctions of a “Bouncing Ball” Type”, Trudy Steklov MIAN, 95, 1968, 106–118 | MR | Zbl

[10] “Formula for Eigenfrequences of Nonfocal Resonator with Cilindric Mirrors, Taking into Account the Aberration of the Mirrors”, Optics and Spectroscopy, 24:3 (1968), 453–454

[11] “Spectral Degeneracy and “Small Denominators” in the Asymptotics of Eigenfunctions of “Bouncing Ball” Type”, Vestn. LGU, Ser. Math., 24:7 (1969), 23–24 | MR

[12] “Eigenfunctions with Given Caustic”, J. of Comput. Math. and Math. Phys., 10:2 (1970), 362–373 | MR | Zbl

[13] “Asymptotics of a Series of the Laplacian's Eigenfunctions Corresponding to the Closed Invariant Curve of the "Billiard Problem”, Probl. Math. Phys. LGU, 1971, no. 5, 72–91 | Zbl

[14] “Short-wave Asymptotics of Eigenfrequences of Membrane. A Series of Eigenfrequences Constucted on Smooth Closed Invariant Curve of the Billiard Problem”, Transactions of the 5th All-Union Symposium of Wave Propogation and Diffraction, Nauka, Leningrad, 1971, 134–143 | Zbl

[15] “On the Asymptotics of the Eigenfunctions of the Laplacian”, Soviet Math. Dokl., 12:5 (1971), 1569–1572 | Zbl

[16] “Existance of the Continuum of Closed Invariant Curves for the Convex Billiard”, Usp. Mat. Nauk, 27:3(165) (1972), 201–202 | MR

[17] “How for the Two–Mirror Resonator the Quality of the General Ellipticity of the System of Beams is connected with the Spectrum”, Zap. Nauchn. Semin. LOMI, 25, 1972, 111–115 (with N. V. Svanidze)

[18] “Construction of the Asymptotics for a Series of the Laplacian's Eigenfunctions Corresponding to the Elliptic Periodical Trajectory of the “Billiard Problem””, Probl. Math. Phys., LGU, 1973, no. 6, 90–100

[19] “The Existance of Caustics for the Billiard Problem in a Convex Domain”, Math. USSR Izv., 7:1 (1973), 185–214 | DOI

[20] “Asymptotics of the Eigenvalues of the Laplacian and Quasimodes. A Series of Quasimodes Corresponding to a Cystem of Caustics Close to the Boundary of the Domain”, Math. USSR Izv., 7:2 (1973), 439–466 | DOI

[21] “Existance of the Infinite Number of the Elliptic and the Hyperbolic Trajectories for the Convex Billiard”, Funkt. Analiz Pril., 7:2 (1973), 20–27 (with M. M. Dvorin) | MR | Zbl

[22] “Short-wave Asymptotics of Eigenfrequences of an Oscillating Membrane, Constructed According to a Family of Invariant Curves”, 6th All-Union Symposium of Wave Propagation and Diffraction, V. 1, Tzakhkadzor, 1973, 40–45

[23] “Asymptotics of Eigenfunctions of the Laplasian on the Torus”, Sb. Vopr. Dynam. Teor. Raspr. Seism. Voln, 14, Nauka, Leningrad, 1974, 84–108

[24] “To Moser Theorem about Invariant Curves”, Sb. Vopr. Dynam. Teor. Raspr. Seism. Voln, 14, Nauka, Leningrad, 1974, 109–120

[25] “Asymptotics of a Series of the Laplacian's Eigenfunctions Connected with the Family of Invariant Curves, I”, Probl. Math. Phys. LGU, 1974, no. 7, 39–65

[26] “Asymptotics of a Series of the Laplacian's Eigenfunctions Connected with the Family of Invariant Curves, II”, Probl. Math. Phis. LGU, 1974, no. 7, 65–79 (with Yu. B. Yanushanetz)

[27] “Asymptotics of the Width of Gaps in the Spectrum of the Sturm–Liouville Operator with a Periodic Potential”, Soviet Math. Dokl., 15:2 (1974), 649–653 (with T. F. Pankratova) | Zbl

[28] “The Counterexample to the Hypothesis of V. I. Arnold about Eigenoscillations of a Membrane”, Zap. Nauchn. Semin. LOMI, 51, 1975, 134–137 | MR | Zbl

[29] “The Normal Forms and the Versal Deformations for the Hill's Equation”, Funkt. Analis Pril., 9:4 (1975), 41–48 (with T. F. Pankratova) | MR | Zbl

[30] “Asymtotics of a Series of the Laplacian's Eigenfunctions Connected with the Family of the Invariant Curves, III”, Probl. Math. Phys. LGU, 1976, no. 8, 92–109 (with Yu. B. Janushanetz)

[31] “The examples of the Diffeomorphisms of the Circle”, Vestn. LGU, Ser. Mathrm., Mech., and Astronomy, 1977, no. 1, 49–55 | MR

[32] “Variaton of the Wave Equation”, 7th All-Union Symposium of Wave Propagation and Diffraction, Abstracts of the papers, 2, Moscow, 1977, 26–29 (with T. F. Pankratova)

[33] The Kolmogorov–Arnold–Moser(KAM)-Theory and Eigenfunctions of the Laplacian, Thesis II Manuscript., LOMI, Leningrad, 1977

[34] “The Esimates of the Widths of Gaps in the Spectrum of the Laplasian”, Dokl. Akad. Nauk SSSR, 245:1 (1979), 20–23 | MR | Zbl

[35] “About an Estimate of $N^*(\lambda)$ for a Series of Quasimodes of the Laplacian”, Probl. Math. Phys. LGU, 1979, no. 9, 64–75

[36] “A Convex Billiard and Eigenfunctions of the Laplasian”, Usp. Mat. Nauk, 35:1 (1980)

[37] “A Complex Eikonal and Losses in the Open Resonators”, 8th All-Union Symposium of Wave propagation and Diffraction, Abstracts of the Papers, 1, M., 1981, 209–212

[38] “Investigation of the Spectrums of a “Bouncing Ball” and of a "Whispering Gallery”, 8th All-Union Symposium of Wave propagation and Diffraction, Absracts of the Papers, M., 1981, 220–223 (with T. F. Pankratova, M. B. Tabanov, D. Ya. Terman)

[39] “About an Estimate of a Remainder in the H.Weyl's Formula”, Funkt. Anal. Pril., 15:4 (1981), 81–82 (with D. Ja. Terman) | MR | Zbl

[40] “Diffraction Losses in the Open Resonators. Geometrical Point of View”, Dokl. Akad. Nauk SSSR, 258:5 (1981), 1089–1092 | MR

[41] A Convex Billiard and Eigenfunctions of the Laplacian, A monograph., LGU, 1981

[42] “About a Number of Quasimodes of a “Bouncing Ball” Type”, Zap Nauchn. Semin. LOMI, 117, Nauka, Leningrad, 1981, 172–182 | MR | Zbl

[43] “Radiation of an Open Resonator Formed by the Slightly Curved Cylindric Mirrors,”, X All-Union Accustic Conference, Sec. A, Moscow, 1983, 13–16 (with M. B. Tabanov)

[44] “Asymptotics of the Nonphysical Eigenfunctios of the Laplacian in a Domai n Similar to a Strip”, Usp. Mat. Nauk, 38:5 (1983), 163–164 (with M. B. Tabanov)

[45] Asymptotic Formulas for the Losses on Radiation from the Qpen Resonator Formed by the Slightly Curved Cylindric Mirrors, I, Dep. VINITI 3828–83, 1983 (with M. B. Tabanov)

[46] Percival Variational Principle for Invariant Measures and Commensurate-Incommensurate Phase Transitions in One-Dimensional Chains, Dep. VINITI 5341–83, 1983 (with D. Ja. Terman)

[47] “Percival Variational Principle for Invariant Measures and Commensurate-Incommensurate Phase Transitions in One-Dimensional Chains”, Comm. Math. Phys., 94:4 (1984), 511–522 (with D. Ja. Terman) | DOI | MR | Zbl

[48] The Separatrices Splitting for the Stadard Chirikov's Map, Dep. VINITI 6372–84, 1984

[49] The Separatrices Splitting for a Standard and a Semi-Standard Map, Dep. VINITI 4027–85, 1985 (with M. B. Tabanov, I. G. Shakhmanski) | Zbl

[50] “A Complex Quantation in Proplemes with Radiation, Modes Splitting and in Periodical Wavegides”, IX All-Union Symposium of Wave Propogation and Diffraction Telavi, Abstracts of the Papers, 2, 1985, 522–525 (with M. B. Tabanov)

[51] “A Complex Billiard”, Probl. Mat. Phys. LGU, 1986, no. 11, 138–164 | MR | Zbl

[52] “The Separatrices Splitting for the Standard Map”, All-Union Conference “Modern Questions of Mechanics and Tecnology”, VINITI, Moscow, 1986, 78 (with M. B. Tabanov, I. G. Scakhmanski)

[53] “The Semi-Standard Map as a Complex Dynamical System”, Usp. Mat. Nauk, 41:4 (1986), 206 (with M. B. Tabanov, I. G. Shakhmanski)

[54] Amer. Math. Soc. Transl. (2), 157, 1993, 27–35 | MR | Zbl

[55] “Quasi-Classical Asymptotics of Eigenfunctions”, Sovr. Probl. Matematiki.. Fundam. Napr., 34, VINITI, M., 1988, 135–174

[56] “The Complex Separatice Splitting”, Funct. Anal. Pril., 22:2 (1988), 83–84 | DOI | MR

[57] “About a Signature of a Symmetrical Inverse Matrix”, Mat. Zametki, 44:2 (1988), 202–207 | Zbl

[58] “The Analytical Integrals of a Semi-Standard Map and the Splitting of Separatrices”, Algebra Analiz, 1:2 (1989), 116–131

[59] “The Separatrices Splitting and the Width of the Instability Zone for the Standard Chirikov's Map. Nonlinesr World”, Proceedings of the IV International Workshop on Nonlinear and Turbulent Processes in Physics, Vol. 2, Naukova Dumka, Kiev, 1989, 284–286 | Zbl

[60] “Splitting of Separatrices for Standard and Semistandard Mappings”, Physica D, 40 (1989), 235–248 | DOI | MR | Zbl

[61] “Mathematical models of critical phenomena”, Physics on the Threshold of New Discoveries, ed. L. N. Labzovskii, LGU, Leningrad, 1990, 279–301

[62] Soviet Math. Dokl., 42:1 (1991), 5–7 | MR | Zbl

[63] “Exponentially small splitting of separatrices in Hamiltonian systems”, Nonlinear Oscillations of Mechanical Systems II All-Union Conference, Abstracts of of papers. Part 1 (September 1990), Gorkii, 1990, 50 (with V. G. Gelfreich, M. B. Tabanov)

[64] “Exponentially small splittings in Hamiltonian systems”, Chaos, 1:2 (1991), 137–142 (with V. G. Gelfreich, M. B. Tabanov) | DOI | MR | Zbl

[65] Exponential Splitting of Separatrices and an Analytic Integral for the Semistandard Map, Preprint, University Paris VII, 1991

[66] Resurgence of the Separatrices of the Semistandard Map, Preprint ETH, Zuerich, 1991

[67] “An analytic integral along the separatrix of the semistandard map: existence and an exponential estimate for the distance between the stable and unstable separatrices”, Algebra Analiz, 4:4 (1992), 110–142 ; St. Petersburg Math. J., 4:4 (1993), 721–748 | MR | Zbl

[68] “Fern-like structures in the wild set of the standard and semistandard maps in $C^2$”, Int. J. of Bifurcation and Chaos, 2:2 (1992), 353–370 (with V. G. Gelreich, C. Simo, M. B. Tabanov) | DOI | MR

[69] Refined formula to separatrix splitting for the standard map, Warwick Preprints: 59/1992, 1992 (with V. G. Gelfreich, N. V. Svanidze) | Zbl

[70] “Resurgent approach to the separatrices splitting”, EQUADIFF 91 International Conference on Differential Equations, Vol. 1 (Barcelona, Spain, 26–31 August 1991), eds. C. Perelló, C. Simó, J. Solá-Morales, World Scientific, Singapore, New Jersey, London, Hong Kong, 1993, 163–176 | MR | Zbl

[71] KAM Theory and Semiclassical Approximation to Eigenfunctions, with Addendum by A. I. Shnirelman, Ergebnisse der Mathematik und ihrer Grenzgebiete, 24, Springer Verlag, Berlin, 1993 | MR

[72] Some remarks concerning the main problem of Hamiltonian dynamics with two degrees of freedom, Université de Nice-Sophia-Antipolos, U.R.A au C.N.R.S. No 168, Jean-Alexandre Dieudonné. Prépublication No 343, 1993

[73] Model map and its separatrices, Unpublished, 1993

[74] Existence of ferns, Universitat de Barcelona. Mathematics Preprint Series No 137, June 1993

[75] Separatrix splitting via résurgence, technical paper, Unpublished paper Barcelona, June 1993

[76] “Complexified quantum rules”, Sémin. Théor. Spectr. Géom., 11, Université de Grenoble 1, Saint, 1993, 133–145 (with D. Ya. Terman) | MR | Zbl

[77] “Recent results on the separatrix splitting for the standard map”, Sémin. Théor. Spectr. Géom., 11, Université de Grenoble 1, Saint, 1993, 157–165 | MR | Zbl

[78] The growth of the norms of the products of random matrices, Warwick Preprints: 80/1993, December 1993

[79] “A refined formula for the separatrix splitting for the standard map”, Physica D, 71:1–2 (1994), 82–101 (with V. G. Gelfreich, N. V. Svanidze) | MR | Zbl

[80] Positive entropy for the standard map, I, Prépublications 94-47 Université de Paris-Sud Mathématiques Bâtiment 425 91405 ORSAY France, 1994

[81] Jumping Folds Phenomenon in Area-Preserving Maps, PennState, Department of Mathematics, Report No PM 190, May, 1995

[82] Interfering combs and a multiple horseshoe, Universität Augsburg, Institut für Mathematik, Report No 333, 1995

[83] “Positive entropy for the standard map”, Russian Math. Surv., 50:4(304) (1995), 85

[84] A stable foliation to infinity in the complexified phase space of the standard map, Universitat de Barcelona, Mathematics Preprint Series No 183, 1995 (with M. Pankratov)

[85] “Homoclinic orbits in the complex domain”, International Journal of Bifurcation and Chaos, 7:2 (1997), 253–274 (with C. Simó) ; Universitat de Barcelona, Mathematics Preprint Series No 203, May 1996 | DOI | MR | Zbl

[86] “Interfering combs and a multiple horseshoe”, Regular and Chaotic Dynamics, 2:2 (1997), 3–13 | MR

[87] “Visualization of a hyperbolic structure in area-preserving maps”, Regular and Chaotic Dynamics, 2:3–4 (1997), 47–61 (with A. Giorgilli, C. Simo) | MR | Zbl

[88] Splitting of separatrices for the Chirikov's standard map, http://citeseer.ist.psu.edu/giorgilli99some.html

[89] “Existence and visualization of a hyperbolic structure in area-preserving maps”, Proceedings of the Second Brussels Meeting on Integrabilty and Chaos in Discrete Systems (Brussels, 2–6 July 1997), Chaos, Solitons and Fractals, 11, 2000, 237–240 | MR | Zbl

[90] “Making fractals fat”, Regular and Chaotic Dynamics, 4:1 (1999), 51–69 ; Universitat de Barcelona. Mathematics Preprint Series No 258, October 1998 | DOI | MR | Zbl

[91] “Semiclassical Asymptotics of Eigenfunctions”, Partial Differential Equations V, Encyclopaedia of Mathematical Sciences, 34, Springer, Berlin, 1999, 133–171

[92] “Existence and visualization of a hyperbolic structure in area-preserving maps”, Integrability and chaos in discrete systems (Brussels, 2–6 July 1997), Chaos, Solitons and Fractals, 11, 2000, 237–240 | MR | Zbl

[93] “Some remarks on the problem of ergodicity of the Standard Map”, Phys. Lett. A, 272 (2000), 359–367 ; (with A. Giorgilli) http://citeseer.ist.psu.edu/giorgilli99some.html | DOI | MR | Zbl

[94] “Existence of complex homoclinic points”, Regular and Chaotic Dynamics, 5:4 (2000), 383–400 (with N. N. Igotti) | DOI | MR | Zbl

[95] A remark on “Some remarks on the problem of ergodicity of the Standard Map”, http://citeseer.ist.psu.edu/giorgilli99some.html

[96] “Splitting of separatrices: perturbation theory and exponential smallness”, Uspekhi Mat. Nauk, 56:3(339) (2001), 79–142 (with V. G. Gelfreich) | MR