Edit Profile (opens in new tab) Berkolaiko, Gregory Co-Author Distance Author ID: berkolaiko.gregory Published as: Berkolaiko, Gregory; Berkolaiko, G. External Links: ORCID Documents Indexed: 74 Publications since 1996, including 1 Book and 7 Additional arXiv Preprints 1 Contribution as Editor Co-Authors: 44 Co-Authors with 55 Joint Publications 1,227 Co-Co-Authors all top 5 Co-Authors 9 single-authored 9 Rodkina, Alexandra 7 Band, Ram 5 Cox, Graham 5 Kuchment, Peter A. 5 Smilansky, Uzy 4 Appleby, John A. D. 4 Keating, Jonathan Peter 4 Marzuola, Jeremy Louis 3 Ettehad, Mahmood 3 Havlin, Shlomo 3 Kelly, Cónall 3 Kennedy, James Bernard 3 Kurasov, Pavel B. 3 Liu, Wen 3 Mugnolo, Delio 2 Alon, Lior 2 Buckwar, Evelyn 2 Canzani, Yaiza 2 Comech, Andrew 2 Duffield, Nick G. 2 Kuipers, Jack B. 2 Latushkin, Yuri 2 Raz, Hillel 2 Sukhtaiev, Selim 2 Weyand, Tracy 1 Bogomolny, E. B. 1 Booton, Laura 1 Borisov, Denis Ivanovich 1 Buldyrev, Sergey V. 1 Colin de Verdière, Yves 1 Fulling, Stephen A. 1 Grinfeld, Michael 1 Harrison, Jon M. 1 Helffer, Bernard 1 Irving, John 1 Joyner, Christopher H. 1 Kha, Minh 1 King, Marshall 1 Manousakis, Kyriakos 1 Parulekar, Advait 1 Pelinovsky, Dmitry Efimovich 1 Sundqvist, Mikael Persson 1 Schanz, Holger 1 Shehter, A. 1 Sukhtayev, Alim 1 Whitney, Robert S. 1 Winn, Brian 1 Zelenko, Igor all top 5 Serials 5 Communications in Mathematical Physics 5 Journal of Mathematical Physics 5 Journal of Physics A: Mathematical and General 5 Journal of Physics A: Mathematical and Theoretical 3 Journal of Mathematical Analysis and Applications 3 Letters in Mathematical Physics 2 Nonlinearity 2 Transactions of the American Mathematical Society 2 Journal of Difference Equations and Applications 2 LMS Journal of Computation and Mathematics 2 Journal of Spectral Theory 1 Inverse Problems 1 Waves in Random Media 1 Advances in Mathematics 1 Journal of Combinatorial Theory. Series A 1 Proceedings of the American Mathematical Society 1 Studies in Applied Mathematics 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Dynamics and Stability of Systems 1 SIAM Journal on Matrix Analysis and Applications 1 The Journal of Geometric Analysis 1 Geometric and Functional Analysis. GAFA 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Calculus of Variations and Partial Differential Equations 1 Discrete and Continuous Dynamical Systems 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 New Journal of Physics 1 Annales Henri Poincaré 1 Stochastics 1 Contemporary Mathematics 1 Mathematical Surveys and Monographs 1 Mathematical Modelling of Natural Phenomena 1 Analysis & PDE 1 Analysis and Mathematical Physics 1 Pure and Applied Analysis all top 5 Fields 38 Quantum theory (81-XX) 21 Ordinary differential equations (34-XX) 20 Combinatorics (05-XX) 17 Partial differential equations (35-XX) 12 Dynamical systems and ergodic theory (37-XX) 9 Operator theory (47-XX) 9 Probability theory and stochastic processes (60-XX) 8 Statistical mechanics, structure of matter (82-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 7 Difference and functional equations (39-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Numerical analysis (65-XX) 4 Systems theory; control (93-XX) 1 General and overarching topics; collections (00-XX) 1 Algebraic geometry (14-XX) 1 Group theory and generalizations (20-XX) 1 Functional analysis (46-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Differential geometry (53-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 58 Publications have been cited 1,060 times in 629 Documents Cited by ▼ Year ▼ Introduction to quantum graphs. Zbl 1318.81005 Berkolaiko, Gregory; Kuchment, Peter 393 2013 Quantum graphs and their applications. Proceedings of an AMS-IMS-SIAM joint summer research conference on quantum graphs and their applications, Snowbird, UT, USA, June 19–23, 2005. Zbl 1098.81007 66 2006 Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths. Zbl 1317.81127 Berkolaiko, G.; Kuchment, P. 46 2012 Surgery principles for the spectral analysis of quantum graphs. Zbl 1451.34029 Berkolaiko, Gregory; Kennedy, James B.; Kurasov, Pavel; Mugnolo, Delio 40 2019 Edge connectivity and the spectral gap of combinatorial and quantum graphs. Zbl 1456.81193 Berkolaiko, Gregory; Kennedy, James B.; Kurasov, Pavel; Mugnolo, Delio 32 2017 An elementary introduction to quantum graphs. Zbl 1388.34020 Berkolaiko, Gregory 31 2017 Symmetry and Dirac points in graphene spectrum. Zbl 1411.35092 Berkolaiko, Gregory; Comech, Andrew 30 2018 Limits of quantum graph operators with shrinking edges. Zbl 1422.81101 Berkolaiko, Gregory; Latushkin, Yuri; Sukhtaiev, Selim 29 2019 The number of nodal domains on quantum graphs as a stability index of graph partitions. Zbl 1244.81026 Band, Ram; Berkolaiko, Gregory; Raz, Hillel; Smilansky, Uzy 27 2012 A lower bound for nodal count on discrete and metric graphs. Zbl 1171.05356 Berkolaiko, Gregory 25 2008 Non-exponential stability and decay rates in nonlinear stochastic difference equations with unbounded noise. Zbl 1177.39020 Appleby, John A. D.; Berkolaiko, Gregory; Rodkina, Alexandra 23 2009 No quantum ergodicity for star graphs. Zbl 1059.81066 Berkolaiko, G.; Keating, J. P.; Winn, B. 22 2004 On spectral stability of solitary waves of nonlinear Dirac equation in 1D. Zbl 1247.35117 Berkolaiko, G.; Comech, A. 22 2012 Simplicity of eigenvalues and non-vanishing of eigenfunctions of a quantum graph. Zbl 1348.81243 Berkolaiko, Gregory; Liu, Wen 21 2017 Star graphs and Šeba billiards. Zbl 1058.81021 Berkolaiko, G.; Bogomolny, E. B.; Keating, Jonathan P. 19 2001 Dynamics of nodal points and the nodal count on a family of quantum graphs. Zbl 1242.81085 Band, Ram; Berkolaiko, Gregory; Smilansky, Uzy 16 2012 Nodal count of graph eigenfunctions via magnetic perturbation. Zbl 1281.35089 Berkolaiko, Gregory 16 2013 Combinatorial theory of the semiclassical evaluation of transport moments. I: Equivalence with the random matrix approach. Zbl 1288.81048 Berkolaiko, G.; Kuipers, J. 16 2013 Form factor for a family of quantum graphs: an expansion to third order. Zbl 1035.81024 Berkolaiko, Gregory; Schanz, Holger; Whitney, Robert S. 15 2003 Stability of eigenvalues of quantum graphs with respect to magnetic perturbation and the nodal count of the eigenfunctions. Zbl 1322.81042 Berkolaiko, Gregory; Weyand, Tracy 14 2014 Critical partitions and nodal deficiency of billiard eigenfunctions. Zbl 1308.35152 Berkolaiko, Gregory; Kuchment, Peter; Smilansky, Uzy 14 2012 Two-point spectral correlations for star graphs. Zbl 0946.81025 Berkolaiko, G.; Keating, Jonathan P. 13 1999 Almost sure convergence of solutions to non-homogeneous stochastic difference equation. Zbl 1099.39002 Berkolaiko, Gregory; Rodkina, Alexandra 13 2006 Almost sure asymptotic stability analysis of the \(\theta\)-Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations. Zbl 1294.60093 Berkolaiko, Gregory; Buckwar, Evelyn; Kelly, Cónall; Rodkina, Alexandra 13 2012 Nodal statistics on quantum graphs. Zbl 1406.81037 Alon, Lior; Band, Ram; Berkolaiko, Gregory 13 2018 Moments of the Wigner delay times. Zbl 1183.81069 Berkolaiko, Gregory; Kuipers, Jack 12 2010 On local stability for a nonlinear difference equation with a non-hyperbolic equilibrium and fading stochastic perturbations. Zbl 1155.39003 Appleby, J.; Berkolaiko, G.; Rodkina, A. 12 2008 Transport moments beyond the leading order. Zbl 1275.82007 Berkolaiko, Gregory; Kuipers, Jack 12 2011 Quantum ergodicity for graphs related to interval maps. Zbl 1122.81037 Berkolaiko, G.; Keating, Jonathan P.; Smilansky, U. 11 2007 Anomalous nodal count and singularities in the dispersion relation of honeycomb graphs. Zbl 1335.81078 Band, Ram; Berkolaiko, Gregory; Weyand, Tracy 11 2015 Vakhitov-Kolokolov and energy vanishing conditions for linear instability of solitary waves in models of classical self-interacting spinor fields. Zbl 1309.35099 Berkolaiko, Gregory; Comech, Andrew; Sukhtayev, Alim 11 2015 Full counting statistics of chaotic cavities from classical action correlations. Zbl 1195.82073 Berkolaiko, G.; Harrison, J. M.; Novaes, M. 11 2008 Edge-localized states on quantum graphs in the limit of large mass. Zbl 1477.35230 Berkolaiko, Gregory; Marzuola, Jeremy L.; Pelinovsky, Dmitry E. 11 2021 Relationship between scattering matrix and spectrum of quantum graphs. Zbl 1204.81077 Berkolaiko, G.; Winn, B. 10 2010 Combinatorial theory of the semiclassical evaluation of transport moments II: algorithmic approach for moment generating functions. Zbl 1288.82053 Berkolaiko, G.; Kuipers, J. 10 2013 Stability of nodal structures in graph eigenfunctions and its relation to the nodal domain count. Zbl 1242.05159 Berkolaiko, Gregory; Raz, Hillel; Smilansky, Uzy 8 2012 Nodal deficiency, spectral flow, and the Dirichlet-to-Neumann map. Zbl 1417.58022 Berkolaiko, Gregory; Cox, Graham; Marzuola, Jeremy L. 7 2019 On asymptotic behavior of solutions to linear discrete stochastic equation. Zbl 1381.93094 Rodkina, Alexandra; Berkolaiko, Gregory 5 2004 Form factor expansion for large graphs: a diagrammatic approach. Zbl 1104.81052 Berkolaiko, Gregory 4 2006 Solving nonlinear recursions. Zbl 0859.65135 Rabinovich, S.; Berkolaiko, G.; Havlin, S. 4 1996 On the aysmptotic behavior of the moments of solutions of stochastic difference equations. Zbl 1127.39003 Appleby, J.; Berkolaiko, G.; Rodkina, A. 4 2007 Spectral shift via “lateral” perturbation. Zbl 1501.47024 Berkolaiko, Gregory; Kuchment, Peter 4 2022 Mathematical aspects of vacuum energy on quantum graphs. Zbl 1154.81020 Berkolaiko, G.; Harrison, Jon M.; Wilson, J. H. 3 2009 Form factor for large quantum graphs: evaluating orbits with time reversal. Zbl 1063.81055 Berkolaiko, Gregory 3 2004 Inequivalent factorizations of permutations. Zbl 1331.05005 Berkolaiko, G.; Irving, J. 3 2016 Three-dimensional elastic beam frames: rigid joint conditions in variational and differential formulation. Zbl 1528.74072 Berkolaiko, Gregory; Ettehad, Mahmood 3 2022 Analysis of Carleman representation of analytical recursions. Zbl 0937.37023 Berkolaiko, G.; Rabinovich, S.; Havlin, S. 2 1998 Spectral gap of doubly stochastic matrices generated from equidistributed unitary matrices. Zbl 1028.82007 Berkolaiko, G. 2 2001 Computing nodal deficiency with a refined Dirichlet-to-Neumann map. Zbl 1495.35130 Berkolaiko, G.; Cox, G.; Helffer, B.; Sundqvist, M. P. 2 2022 Multiplicity of periodic solutions in bistable equations. Zbl 1149.34326 Berkolaiko, Gregory; Grinfeld, Michael 1 2006 Analytical solution of the logistic equation. Zbl 0905.39007 Rabinovich, S.; Berkolaiko, G.; Buldyrev, S.; Shehter, A.; Havlin, S. 1 1997 Dynamics of piecewise linear interval maps with hysteresis. Zbl 0942.37027 Berkolaiko, G. 1 1999 Two constructions of quantum graphs and two types of spectral statistics. Zbl 1154.81337 Berkolaiko, G. 1 2008 Corrigendum: On the use of a discrete form of the Itô formula in the article “Almost sure asymptotic stability analysis of the \(\theta\)-Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations”. Zbl 1297.60044 Berkolaiko, Gregory; Buckwar, Evelyn; Kelly, Cónall; Rodkina, Alexandra 1 2013 Degenerate band edges in periodic quantum graphs. Zbl 1456.81194 Berkolaiko, Gregory; Kha, Minh 1 2020 Locating conical degeneracies in the spectra of parametric self-adjoint matrices. Zbl 1467.65028 Berkolaiko, Gregory; Parulekar, Advait 1 2021 Stability of spectral partitions and the Dirichlet-to-Neumann map. Zbl 1497.58016 Berkolaiko, G.; Canzani, Y.; Cox, G.; Marzuola, J. L. 1 2022 A local test for global extrema in the dispersion relation of a periodic graph. Zbl 1505.35312 Berkolaiko, Gregory; Canzani, Yaiza; Cox, Graham; Marzuola, Jeremy Louis 1 2022 Spectral shift via “lateral” perturbation. Zbl 1501.47024 Berkolaiko, Gregory; Kuchment, Peter 4 2022 Three-dimensional elastic beam frames: rigid joint conditions in variational and differential formulation. Zbl 1528.74072 Berkolaiko, Gregory; Ettehad, Mahmood 3 2022 Computing nodal deficiency with a refined Dirichlet-to-Neumann map. Zbl 1495.35130 Berkolaiko, G.; Cox, G.; Helffer, B.; Sundqvist, M. P. 2 2022 Stability of spectral partitions and the Dirichlet-to-Neumann map. Zbl 1497.58016 Berkolaiko, G.; Canzani, Y.; Cox, G.; Marzuola, J. L. 1 2022 A local test for global extrema in the dispersion relation of a periodic graph. Zbl 1505.35312 Berkolaiko, Gregory; Canzani, Yaiza; Cox, Graham; Marzuola, Jeremy Louis 1 2022 Edge-localized states on quantum graphs in the limit of large mass. Zbl 1477.35230 Berkolaiko, Gregory; Marzuola, Jeremy L.; Pelinovsky, Dmitry E. 11 2021 Locating conical degeneracies in the spectra of parametric self-adjoint matrices. Zbl 1467.65028 Berkolaiko, Gregory; Parulekar, Advait 1 2021 Degenerate band edges in periodic quantum graphs. Zbl 1456.81194 Berkolaiko, Gregory; Kha, Minh 1 2020 Surgery principles for the spectral analysis of quantum graphs. Zbl 1451.34029 Berkolaiko, Gregory; Kennedy, James B.; Kurasov, Pavel; Mugnolo, Delio 40 2019 Limits of quantum graph operators with shrinking edges. Zbl 1422.81101 Berkolaiko, Gregory; Latushkin, Yuri; Sukhtaiev, Selim 29 2019 Nodal deficiency, spectral flow, and the Dirichlet-to-Neumann map. Zbl 1417.58022 Berkolaiko, Gregory; Cox, Graham; Marzuola, Jeremy L. 7 2019 Symmetry and Dirac points in graphene spectrum. Zbl 1411.35092 Berkolaiko, Gregory; Comech, Andrew 30 2018 Nodal statistics on quantum graphs. Zbl 1406.81037 Alon, Lior; Band, Ram; Berkolaiko, Gregory 13 2018 Edge connectivity and the spectral gap of combinatorial and quantum graphs. Zbl 1456.81193 Berkolaiko, Gregory; Kennedy, James B.; Kurasov, Pavel; Mugnolo, Delio 32 2017 An elementary introduction to quantum graphs. Zbl 1388.34020 Berkolaiko, Gregory 31 2017 Simplicity of eigenvalues and non-vanishing of eigenfunctions of a quantum graph. Zbl 1348.81243 Berkolaiko, Gregory; Liu, Wen 21 2017 Inequivalent factorizations of permutations. Zbl 1331.05005 Berkolaiko, G.; Irving, J. 3 2016 Anomalous nodal count and singularities in the dispersion relation of honeycomb graphs. Zbl 1335.81078 Band, Ram; Berkolaiko, Gregory; Weyand, Tracy 11 2015 Vakhitov-Kolokolov and energy vanishing conditions for linear instability of solitary waves in models of classical self-interacting spinor fields. Zbl 1309.35099 Berkolaiko, Gregory; Comech, Andrew; Sukhtayev, Alim 11 2015 Stability of eigenvalues of quantum graphs with respect to magnetic perturbation and the nodal count of the eigenfunctions. Zbl 1322.81042 Berkolaiko, Gregory; Weyand, Tracy 14 2014 Introduction to quantum graphs. Zbl 1318.81005 Berkolaiko, Gregory; Kuchment, Peter 393 2013 Nodal count of graph eigenfunctions via magnetic perturbation. Zbl 1281.35089 Berkolaiko, Gregory 16 2013 Combinatorial theory of the semiclassical evaluation of transport moments. I: Equivalence with the random matrix approach. Zbl 1288.81048 Berkolaiko, G.; Kuipers, J. 16 2013 Combinatorial theory of the semiclassical evaluation of transport moments II: algorithmic approach for moment generating functions. Zbl 1288.82053 Berkolaiko, G.; Kuipers, J. 10 2013 Corrigendum: On the use of a discrete form of the Itô formula in the article “Almost sure asymptotic stability analysis of the \(\theta\)-Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations”. Zbl 1297.60044 Berkolaiko, Gregory; Buckwar, Evelyn; Kelly, Cónall; Rodkina, Alexandra 1 2013 Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths. Zbl 1317.81127 Berkolaiko, G.; Kuchment, P. 46 2012 The number of nodal domains on quantum graphs as a stability index of graph partitions. Zbl 1244.81026 Band, Ram; Berkolaiko, Gregory; Raz, Hillel; Smilansky, Uzy 27 2012 On spectral stability of solitary waves of nonlinear Dirac equation in 1D. Zbl 1247.35117 Berkolaiko, G.; Comech, A. 22 2012 Dynamics of nodal points and the nodal count on a family of quantum graphs. Zbl 1242.81085 Band, Ram; Berkolaiko, Gregory; Smilansky, Uzy 16 2012 Critical partitions and nodal deficiency of billiard eigenfunctions. Zbl 1308.35152 Berkolaiko, Gregory; Kuchment, Peter; Smilansky, Uzy 14 2012 Almost sure asymptotic stability analysis of the \(\theta\)-Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations. Zbl 1294.60093 Berkolaiko, Gregory; Buckwar, Evelyn; Kelly, Cónall; Rodkina, Alexandra 13 2012 Stability of nodal structures in graph eigenfunctions and its relation to the nodal domain count. Zbl 1242.05159 Berkolaiko, Gregory; Raz, Hillel; Smilansky, Uzy 8 2012 Transport moments beyond the leading order. Zbl 1275.82007 Berkolaiko, Gregory; Kuipers, Jack 12 2011 Moments of the Wigner delay times. Zbl 1183.81069 Berkolaiko, Gregory; Kuipers, Jack 12 2010 Relationship between scattering matrix and spectrum of quantum graphs. Zbl 1204.81077 Berkolaiko, G.; Winn, B. 10 2010 Non-exponential stability and decay rates in nonlinear stochastic difference equations with unbounded noise. Zbl 1177.39020 Appleby, John A. D.; Berkolaiko, Gregory; Rodkina, Alexandra 23 2009 Mathematical aspects of vacuum energy on quantum graphs. Zbl 1154.81020 Berkolaiko, G.; Harrison, Jon M.; Wilson, J. H. 3 2009 A lower bound for nodal count on discrete and metric graphs. Zbl 1171.05356 Berkolaiko, Gregory 25 2008 On local stability for a nonlinear difference equation with a non-hyperbolic equilibrium and fading stochastic perturbations. Zbl 1155.39003 Appleby, J.; Berkolaiko, G.; Rodkina, A. 12 2008 Full counting statistics of chaotic cavities from classical action correlations. Zbl 1195.82073 Berkolaiko, G.; Harrison, J. M.; Novaes, M. 11 2008 Two constructions of quantum graphs and two types of spectral statistics. Zbl 1154.81337 Berkolaiko, G. 1 2008 Quantum ergodicity for graphs related to interval maps. Zbl 1122.81037 Berkolaiko, G.; Keating, Jonathan P.; Smilansky, U. 11 2007 On the aysmptotic behavior of the moments of solutions of stochastic difference equations. Zbl 1127.39003 Appleby, J.; Berkolaiko, G.; Rodkina, A. 4 2007 Quantum graphs and their applications. Proceedings of an AMS-IMS-SIAM joint summer research conference on quantum graphs and their applications, Snowbird, UT, USA, June 19–23, 2005. Zbl 1098.81007 66 2006 Almost sure convergence of solutions to non-homogeneous stochastic difference equation. Zbl 1099.39002 Berkolaiko, Gregory; Rodkina, Alexandra 13 2006 Form factor expansion for large graphs: a diagrammatic approach. Zbl 1104.81052 Berkolaiko, Gregory 4 2006 Multiplicity of periodic solutions in bistable equations. Zbl 1149.34326 Berkolaiko, Gregory; Grinfeld, Michael 1 2006 No quantum ergodicity for star graphs. Zbl 1059.81066 Berkolaiko, G.; Keating, J. P.; Winn, B. 22 2004 On asymptotic behavior of solutions to linear discrete stochastic equation. Zbl 1381.93094 Rodkina, Alexandra; Berkolaiko, Gregory 5 2004 Form factor for large quantum graphs: evaluating orbits with time reversal. Zbl 1063.81055 Berkolaiko, Gregory 3 2004 Form factor for a family of quantum graphs: an expansion to third order. Zbl 1035.81024 Berkolaiko, Gregory; Schanz, Holger; Whitney, Robert S. 15 2003 Star graphs and Šeba billiards. Zbl 1058.81021 Berkolaiko, G.; Bogomolny, E. B.; Keating, Jonathan P. 19 2001 Spectral gap of doubly stochastic matrices generated from equidistributed unitary matrices. Zbl 1028.82007 Berkolaiko, G. 2 2001 Two-point spectral correlations for star graphs. Zbl 0946.81025 Berkolaiko, G.; Keating, Jonathan P. 13 1999 Dynamics of piecewise linear interval maps with hysteresis. Zbl 0942.37027 Berkolaiko, G. 1 1999 Analysis of Carleman representation of analytical recursions. Zbl 0937.37023 Berkolaiko, G.; Rabinovich, S.; Havlin, S. 2 1998 Analytical solution of the logistic equation. Zbl 0905.39007 Rabinovich, S.; Berkolaiko, G.; Buldyrev, S.; Shehter, A.; Havlin, S. 1 1997 Solving nonlinear recursions. Zbl 0859.65135 Rabinovich, S.; Berkolaiko, G.; Havlin, S. 4 1996 all cited Publications top 5 cited Publications all top 5 Cited by 673 Authors 30 Berkolaiko, Gregory 26 Exner, Pavel 23 Mugnolo, Delio 22 Rodkina, Alexandra 21 Kurasov, Pavel B. 12 Band, Ram 12 Dovetta, Simone 12 Kennedy, James Bernard 12 Pelinovsky, Dmitry Efimovich 11 Bondarenko, Natalia P. 11 Braverman, Elena 10 Adami, Riccardo 10 Rohleder, Jonathan 10 Smilansky, Uzy 9 Borisov, Denis Ivanovich 9 Cacciapuoti, Claudio 9 Noja, Diego 9 Rabinovich, Vladimir Samuilovich 9 Weinstein, Michael I. 9 Yang, Chuanfu 8 Korotyaev, Evgeny L. 8 Kostenko, Aleksey S. 8 Kuchment, Peter A. 8 Popov, Igor’ Yur’evich 8 Saburova, Natalia 8 Serra, Enrico 8 Tentarelli, Lorenzo 7 Angulo Pava, Jaime 7 Avdonin, Sergeĭ Anatol’evich 7 Pankrashkin, Konstantin 7 Post, Olaf 7 Winn, Brian 6 Drouot, Alexis 6 Goloshchapova, Nataliia 6 Kairzhan, Adilbek 6 Keating, Jonathan Peter 6 Lipovský, Jiří 6 Liu, Wei 6 Mao, Xuerong 6 Marzuola, Jeremy Louis 6 Nicolussi, Noema 6 Plümer, Marvin 6 Tilli, Paolo 5 Baradaran, Marzieh 5 Behrndt, Jussi 5 Comech, Andrew 5 Cox, Graham 5 Gnutzmann, Sven 5 Hussein, Amru 5 Kelly, Cónall 5 Kiselev, Alexander V. 5 Malamud, Mark M. 5 Mezzadri, Francesco 5 Niikuni, Hiroaki 5 Novaes, Marcel 5 Rossi, Julio Daniel 5 Serio, Andrea 5 Shafarevich, Andreĭ Igorevich 5 Tater, Miloš 5 Teplyaev, Alexander 5 Tolchennikov, Anton A. 5 Weyand, Tracy 4 Albeverio, Sergio A. 4 Anantharaman, Nalini 4 Appleby, John A. D. 4 Blinova, Irina V. 4 Bolte, Jens 4 Cavalcante, Márcio André Araújo 4 Cherednichenko, Kirill D. 4 Fefferman, Charles Louis 4 Finco, Domenico 4 Harrell, Evans M. II 4 Harrison, Jon M. 4 Helffer, Bernard 4 Hofmann, Matthias 4 Howard, Peter 4 Ingremeau, Maxime 4 Kerner, Joachim 4 Latushkin, Yuri 4 Lenz, Daniel H. 4 Lotoreichik, Vladimir 4 Muminov, Zahriddin Ishkobilovich 4 Neidhardt, Hagen 4 Pivovarchik, Vyacheslav N. 4 Seifert, Christian 4 Shipman, Stephen P. 4 Sukhtaiev, Selim 4 Turek, Ondřej 3 Allilueva, Anna I. 3 Barrera-Figueroa, Victor 3 Borrelli, William 3 Boussaid, Nabile 3 Carlone, Raffaele 3 Chernyshev, Vsevolod L. 3 Colin de Verdière, Yves 3 Cunden, Fabio Deelan 3 Ershova, Yulia Yu. 3 Ignat, Liviu I. 3 Ishii, Yuta 3 Joly, Patrick ...and 573 more Authors all top 5 Cited in 194 Serials 32 Journal of Physics A: Mathematical and Theoretical 30 Journal of Mathematical Physics 23 Communications in Mathematical Physics 23 Annales Henri Poincaré 22 Journal of Mathematical Analysis and Applications 15 Journal of Differential Equations 14 Letters in Mathematical Physics 13 Analysis and Mathematical Physics 12 Integral Equations and Operator Theory 11 Journal of Spectral Theory 10 Journal of Functional Analysis 9 Calculus of Variations and Partial Differential Equations 9 Russian Journal of Mathematical Physics 8 Nonlinearity 8 Physics Letters. A 8 Proceedings of the American Mathematical Society 7 Reviews in Mathematical Physics 7 Advances in Mathematics 7 SIAM Journal on Mathematical Analysis 7 Journal of Difference Equations and Applications 6 Journal of Computational and Applied Mathematics 6 Transactions of the American Mathematical Society 6 Journal of Mathematical Sciences (New York) 6 Networks and Heterogeneous Media 6 Symmetry 5 Reports on Mathematical Physics 5 Mathematische Nachrichten 5 Physica D 5 Journal of Nonlinear Science 5 Discrete and Continuous Dynamical Systems 5 Discrete and Continuous Dynamical Systems. Series B 4 Applicable Analysis 4 Computers & Mathematics with Applications 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Results in Mathematics 4 Journal of Global Optimization 4 Communications in Partial Differential Equations 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Applied and Computational Harmonic Analysis 4 NoDEA. Nonlinear Differential Equations and Applications 4 Journal of Evolution Equations 4 Communications on Pure and Applied Analysis 4 Multiscale Modeling & Simulation 4 Inverse Problems and Imaging 4 Operators and Matrices 3 Journal of Statistical Physics 3 Studies in Applied Mathematics 3 Doklady Mathematics 3 Mathematical Physics, Analysis and Geometry 3 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 Communications in Nonlinear Science and Numerical Simulation 3 Lobachevskii Journal of Mathematics 3 Quantum Information Processing 3 Advances in Difference Equations 3 Oberwolfach Reports 3 Complex Analysis and Operator Theory 3 Discrete and Continuous Dynamical Systems. Series S 3 Mathematical Control and Related Fields 3 Pure and Applied Analysis 2 Archive for Rational Mechanics and Analysis 2 Journal d’Analyse Mathématique 2 Linear and Multilinear Algebra 2 Mathematical Notes 2 Ukrainian Mathematical Journal 2 Annales de l’Institut Fourier 2 Applied Mathematics and Computation 2 Applied Mathematics and Optimization 2 Automatica 2 Duke Mathematical Journal 2 Journal of the London Mathematical Society. Second Series 2 Mathematische Annalen 2 Mathematics and Computers in Simulation 2 Mathematische Zeitschrift 2 Numerische Mathematik 2 SIAM Journal on Numerical Analysis 2 Systems & Control Letters 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Applied Numerical Mathematics 2 SIAM Journal on Matrix Analysis and Applications 2 Numerical Algorithms 2 Geometric and Functional Analysis. GAFA 2 Annals of Physics 2 Linear Algebra and its Applications 2 SIAM Journal on Applied Mathematics 2 Electronic Journal of Differential Equations (EJDE) 2 St. Petersburg Mathematical Journal 2 Opuscula Mathematica 2 Boletín de la Sociedad Matemática Mexicana. Third Series 2 Chaos 2 Discrete Dynamics in Nature and Society 2 Complex Variables and Elliptic Equations 2 Analysis & PDE 2 Evolution Equations and Control Theory 2 Mathematics in Engineering 1 Communications on Pure and Applied Mathematics 1 Discrete Mathematics 1 International Journal of Engineering Science 1 Journal of Mathematical Biology 1 Mathematical Methods in the Applied Sciences 1 Physica A ...and 94 more Serials all top 5 Cited in 48 Fields 309 Quantum theory (81-XX) 283 Partial differential equations (35-XX) 164 Ordinary differential equations (34-XX) 137 Operator theory (47-XX) 131 Combinatorics (05-XX) 53 Probability theory and stochastic processes (60-XX) 50 Global analysis, analysis on manifolds (58-XX) 45 Dynamical systems and ergodic theory (37-XX) 40 Statistical mechanics, structure of matter (82-XX) 38 Calculus of variations and optimal control; optimization (49-XX) 35 Difference and functional equations (39-XX) 34 Systems theory; control (93-XX) 33 Numerical analysis (65-XX) 26 Functional analysis (46-XX) 20 Linear and multilinear algebra; matrix theory (15-XX) 10 Biology and other natural sciences (92-XX) 9 Measure and integration (28-XX) 9 Approximations and expansions (41-XX) 9 Optics, electromagnetic theory (78-XX) 7 Mechanics of deformable solids (74-XX) 6 Potential theory (31-XX) 6 Operations research, mathematical programming (90-XX) 5 Real functions (26-XX) 5 Convex and discrete geometry (52-XX) 5 Mechanics of particles and systems (70-XX) 5 Information and communication theory, circuits (94-XX) 4 General and overarching topics; collections (00-XX) 4 Number theory (11-XX) 3 Algebraic geometry (14-XX) 3 Nonassociative rings and algebras (17-XX) 3 Group theory and generalizations (20-XX) 3 Topological groups, Lie groups (22-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Integral equations (45-XX) 3 Differential geometry (53-XX) 2 Geometry (51-XX) 2 Statistics (62-XX) 2 Fluid mechanics (76-XX) 1 Associative rings and algebras (16-XX) 1 Category theory; homological algebra (18-XX) 1 \(K\)-theory (19-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Computer science (68-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year