Edit Profile (opens in new tab) Rüssmann, Helmut Co-Author Distance Author ID: russmann.helmut Published as: Rüssmann, Helmut; Rüssmann, H.; Ruessmann, Helmut; Rüßmann, Helmut; Ruessmann, H. more...less External Links: MGP · Wikidata · GND Documents Indexed: 29 Publications since 1959 Reviewing Activity: 79 Reviews Co-Authors: 2 Co-Authors with 2 Joint Publications 55 Co-Co-Authors Co-Authors 27 single-authored 1 Wermuth, Nanny 1 Zehnder, Eduard J. all top 5 Serials 3 Mathematische Annalen 3 Celestial Mechanics 2 Ergodic Theory and Dynamical Systems 2 Regular and Chaotic Dynamics 1 Archive for Rational Mechanics and Analysis 1 Communications in Mathematical Physics 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Scandinavian Journal of Statistics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Mathematische Zeitschrift 1 Nachrichten der Akademie der Wissenschaften in Göttingen. II. Mathematisch-Physikalische Klasse 1 Journal of Mathematics and Mechanics 1 Zeitschrift für Astrophysik 1 Discrete and Continuous Dynamical Systems. Series S all top 5 Fields 9 Dynamical systems and ergodic theory (37-XX) 9 Mechanics of particles and systems (70-XX) 4 Ordinary differential equations (34-XX) 3 Difference and functional equations (39-XX) 2 Functions of a complex variable (30-XX) 2 Partial differential equations (35-XX) 2 Approximations and expansions (41-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Statistics (62-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 24 Publications have been cited 389 times in 307 Documents Cited by ▼ Year ▼ Invariant tori in non-degenerate nearly integrable Hamiltonian systems. Zbl 0992.37050 Rüssmann, H. 107 2001 Über das Verhalten analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung. Zbl 0124.04701 Rüssmann, H. 34 1964 Stability of elliptic fixed points of analytic area-preserving mappings under the Bruno condition. Zbl 1030.37040 Rüssmann, Helmut 31 2002 Über die Normalform analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung. Zbl 0143.10801 Rüssmann, H. 27 1967 On optimal estimates for the solutions of linear partial differential equations of first order with constant coefficients on the torus. Zbl 0319.35017 Rüssmann, Helmut 24 1975 On optimal estimates for the solutions of linear difference equations on the circle. Zbl 0343.39002 Rüssmann, Helmut 23 1976 KAM iteration with nearly infinitely small steps in dynamical systems of polynomial character. Zbl 1221.37114 Rüssmann, Helmut 19 2010 On the one-dimensional Schrödinger equation with a quasi-periodic potential. Zbl 0477.34007 Ruessmann, Helmut 17 1980 On a new proof of Moser’s twist mapping theorem. Zbl 0353.34008 Rüssmann, Helmut 15 1976 Kleine Nenner. II: Bemerkungen zur Newtonschen Methode. Zbl 0255.30003 Rüssmann, Helmut 15 1972 On the existence of invariant curves of twist mappings of an annulus. Zbl 0531.58041 Rüssmann, Helmut 12 1983 Über die Iteration analytischer Funktionen. Zbl 0186.47704 Rüssmann, H. 11 1967 Convergent transformations into a normal form in analytic Hamiltonian systems with two degrees of freedom on the zero energy surface near degenerate elliptic singularities. Zbl 1087.37050 Rüssmann, Helmut 10 2004 Non-degeneracy in the perturbation theory of integrable dynamical systems. Zbl 0689.34039 Rüssmann, Helmut 7 1989 Über die Existenz einer Normalform inhaltstreuer elliptischer Transformationen. Zbl 0084.19904 Rüssmann, Helmut 7 1959 On the frequencies of quasi periodic solutions of analytic nearly integrable Hamiltonian systems. Zbl 0797.58028 Rüssmann, Helmut 6 1994 On an inequality for trigonometric polynomials in several variables. Zbl 0695.42003 Rüssmann, Helmut 5 1990 Addendum to “Invariant tori in non-degenerate nearly integrable Hamiltonian systems”. Zbl 1078.30508 Rüssmann, H. 5 2005 Über einen Vergleichssatz für lineare gewöhnliche Differentialgleichungen. Zbl 0183.35902 Rüssmann, H. 4 1969 Konvergente Reihenentwicklungen in der Störungstheorie der Himmelsmechanik. Zbl 0414.70009 Rüssmann, Helmut 3 1979 Nondegeneracy in the perturbation theory of integrable dynamical systems. Zbl 0689.70012 Rüssmann, Helmut 3 1990 Eigenanalysis of symmetrizable matrix products: A result with statistical applications. Zbl 0797.15009 Wermuth, Nanny; Rüssmann, Helmut 2 1993 On a normal form of symmetric maps of \([0,1]\). Zbl 0429.26002 Rüssmann, H.; Zehnder, E. 1 1980 Über die Existenz kanonischer Transformationen bei mehreren unabhängigen Veränderlichen. Zbl 0112.15502 Rüssmann, Helmut 1 1961 KAM iteration with nearly infinitely small steps in dynamical systems of polynomial character. Zbl 1221.37114 Rüssmann, Helmut 19 2010 Addendum to “Invariant tori in non-degenerate nearly integrable Hamiltonian systems”. Zbl 1078.30508 Rüssmann, H. 5 2005 Convergent transformations into a normal form in analytic Hamiltonian systems with two degrees of freedom on the zero energy surface near degenerate elliptic singularities. Zbl 1087.37050 Rüssmann, Helmut 10 2004 Stability of elliptic fixed points of analytic area-preserving mappings under the Bruno condition. Zbl 1030.37040 Rüssmann, Helmut 31 2002 Invariant tori in non-degenerate nearly integrable Hamiltonian systems. Zbl 0992.37050 Rüssmann, H. 107 2001 On the frequencies of quasi periodic solutions of analytic nearly integrable Hamiltonian systems. Zbl 0797.58028 Rüssmann, Helmut 6 1994 Eigenanalysis of symmetrizable matrix products: A result with statistical applications. Zbl 0797.15009 Wermuth, Nanny; Rüssmann, Helmut 2 1993 On an inequality for trigonometric polynomials in several variables. Zbl 0695.42003 Rüssmann, Helmut 5 1990 Nondegeneracy in the perturbation theory of integrable dynamical systems. Zbl 0689.70012 Rüssmann, Helmut 3 1990 Non-degeneracy in the perturbation theory of integrable dynamical systems. Zbl 0689.34039 Rüssmann, Helmut 7 1989 On the existence of invariant curves of twist mappings of an annulus. Zbl 0531.58041 Rüssmann, Helmut 12 1983 On the one-dimensional Schrödinger equation with a quasi-periodic potential. Zbl 0477.34007 Ruessmann, Helmut 17 1980 On a normal form of symmetric maps of \([0,1]\). Zbl 0429.26002 Rüssmann, H.; Zehnder, E. 1 1980 Konvergente Reihenentwicklungen in der Störungstheorie der Himmelsmechanik. Zbl 0414.70009 Rüssmann, Helmut 3 1979 On optimal estimates for the solutions of linear difference equations on the circle. Zbl 0343.39002 Rüssmann, Helmut 23 1976 On a new proof of Moser’s twist mapping theorem. Zbl 0353.34008 Rüssmann, Helmut 15 1976 On optimal estimates for the solutions of linear partial differential equations of first order with constant coefficients on the torus. Zbl 0319.35017 Rüssmann, Helmut 24 1975 Kleine Nenner. II: Bemerkungen zur Newtonschen Methode. Zbl 0255.30003 Rüssmann, Helmut 15 1972 Über einen Vergleichssatz für lineare gewöhnliche Differentialgleichungen. Zbl 0183.35902 Rüssmann, H. 4 1969 Über die Normalform analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung. Zbl 0143.10801 Rüssmann, H. 27 1967 Über die Iteration analytischer Funktionen. Zbl 0186.47704 Rüssmann, H. 11 1967 Über das Verhalten analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung. Zbl 0124.04701 Rüssmann, H. 34 1964 Über die Existenz kanonischer Transformationen bei mehreren unabhängigen Veränderlichen. Zbl 0112.15502 Rüssmann, Helmut 1 1961 Über die Existenz einer Normalform inhaltstreuer elliptischer Transformationen. Zbl 0084.19904 Rüssmann, Helmut 7 1959 all cited Publications top 5 cited Publications all top 5 Cited by 283 Authors 32 Xu, Junxiang 18 de la Llave, Rafael 18 Zhang, Dongfeng 12 Bounemoura, Abed Bounemoura 9 Berti, Massimiliano 9 Si, Wen 8 Haro, Àlex 8 Stolovitch, Laurent 7 Celletti, Alessandra 7 Chierchia, Luigi 7 Fayad, Bassam R. 7 Hanßmann, Heinz 7 Si, Jianguo 7 You, Jiangong 6 Broer, Henk W. 6 Li, Yong 5 Li, Jia 5 Ma, Zhichao 4 Bambusi, Dario 4 Calleja, Renato C. 4 Gentile, Guido 4 Gong, Xianghong 4 Huang, Peng 4 Li, Xuemei 4 Montalto, Riccardo 4 Pinzari, Gabriella 4 Rüssmann, Helmut 4 Salomão, Pedro Antonio Santoro 4 Sevryuk, Mikhail Borisovich 4 Wu, Hao 3 Eliasson, L. Hakan 3 Fontich, Ernest 3 Gallavotti, Giovanni M. 3 Garay, Mauricio Demian 3 Graffi, Sandro 3 Grotta Ragazzo, Clodoaldo 3 Herman, Michael Robert 3 Krikorian, Raphaël 3 Li, Xiong 3 Lu, Xuezhu 3 Luque, Alejandro 3 Massetti, Jessica Elisa 3 Nguyen Tien Zung 3 Pelayo, Alvaro 3 Pöschel, Jürgen 3 Sire, Yannick 3 Xu, XinDong 2 Baldi, Pietro 2 Bernard, Patrick 2 Butler, Leo T. 2 de Paulo, Naiara V. 2 Ecalle, Jean P. 2 Farré, Gerard 2 Féjoz, Jacques 2 Figueras, Jordi-Lluís 2 Fischler, Stéphane 2 González-Enríquez, Alejandra 2 Ivanov, Alexey V. 2 Koch, Hans-Friedrich 2 Kocić, Saša 2 Lerman, Lev 2 Li, Jing 2 Lopes Dias, João 2 Marmi, Stefano 2 Maspero, Alberto 2 Moser, Jürgen K. 2 Niederman, Laurent 2 Obaya, Rafael 2 Paul, Thierry 2 Qian, Weichao 2 Raissy, Jasmin 2 Saprykina, Maria 2 Shang, Zaijiu 2 Shi, Yunfeng 2 Treshchev, Dmitriĭ Valer’evich 2 Verstringe, Freek 2 Villanueva, Jordi 2 Vũ Ngọc, San 2 Wang, Kun 2 Yang, Xue 2 Yi, Yingfei 2 Yin, Wanke 2 Yuan, Xiaoping 2 Zehnder, Eduard J. 2 Zhang, Yuan 2 Zhao, Xuefeng 2 Zhu, Chunpeng 1 Abate, Marco 1 Anderson, Rodney L. 1 Arioli, Gianni 1 Arnaud, Marie-Claude 1 Avila, Artur 1 Baker, Irvine Noel 1 Barata, João C. A. 1 Bardelle, C. 1 Barone, Fiorella 1 Barrar, Richard B. 1 Bartlett, James H. jun. 1 Bazzani, Armando 1 Bellissard, Jean V. ...and 183 more Authors all top 5 Cited in 106 Serials 34 Journal of Differential Equations 19 Regular and Chaotic Dynamics 16 Communications in Mathematical Physics 11 Journal of Mathematical Physics 10 Journal of Dynamics and Differential Equations 10 Discrete and Continuous Dynamical Systems 10 Qualitative Theory of Dynamical Systems 8 Nonlinearity 7 Mathematische Zeitschrift 6 Ergodic Theory and Dynamical Systems 6 Journal of Nonlinear Science 5 Memoirs of the American Mathematical Society 5 Proceedings of the American Mathematical Society 5 SIAM Journal on Applied Dynamical Systems 4 Archive for Rational Mechanics and Analysis 4 Advances in Mathematics 4 Inventiones Mathematicae 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Transactions of the American Mathematical Society 4 Bulletin of the American Mathematical Society. New Series 4 Science China. Mathematics 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Annales de l’Institut Fourier 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Publications Mathématiques 3 Physica D 3 Celestial Mechanics 3 Celestial Mechanics and Dynamical Astronomy 3 Chaos 3 Communications in Nonlinear Science and Numerical Simulation 3 Annales Henri Poincaré 3 Communications on Pure and Applied Analysis 2 Journal of Mathematical Analysis and Applications 2 Chaos, Solitons and Fractals 2 Bulletin de la Société Mathématique de France 2 Duke Mathematical Journal 2 Journal of Functional Analysis 2 Journal für die Reine und Angewandte Mathematik 2 Mathematische Annalen 2 The Journal of Geometric Analysis 2 Annales de l’Institut Henri Poincaré. Physique Théorique 2 Indagationes Mathematicae. New Series 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 Acta Mathematica Sinica. English Series 2 Dynamical Systems 2 Foundations of Computational Mathematics 2 Discrete and Continuous Dynamical Systems. Series B 2 Proceedings of the Steklov Institute of Mathematics 2 Frontiers of Mathematics in China 2 Bollettino dell’Unione Matematica Italiana 1 Applicable Analysis 1 Classical and Quantum Gravity 1 Communications on Pure and Applied Mathematics 1 Journal of Applied Mathematics and Mechanics 1 Journal of Statistical Physics 1 Letters in Mathematical Physics 1 Lithuanian Mathematical Journal 1 Mathematical Methods in the Applied Sciences 1 Studia Mathematica 1 Ukraïns’kyĭ Matematychnyĭ Zhurnal 1 The Mathematical Intelligencer 1 Acta Mathematica 1 Archiv der Mathematik 1 Boletim da Sociedade Brasileira de Matemática 1 Compositio Mathematica 1 Kodai Mathematical Journal 1 Manuscripta Mathematica 1 Mathematics and Computers in Simulation 1 Meccanica 1 Numerische Mathematik 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Chinese Annals of Mathematics. Series B 1 Acta Applicandae Mathematicae 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Journal of the American Mathematical Society 1 Dynamics and Stability of Systems 1 Journal of the Ramanujan Mathematical Society 1 Science in China. Series A 1 Aequationes Mathematicae 1 Pattern Recognition 1 Mémoires de la Société Mathématique de France. Nouvelle Série 1 Computational Statistics and Data Analysis 1 Topological Methods in Nonlinear Analysis 1 Russian Journal of Mathematical Physics 1 Journal of Mathematical Sciences (New York) 1 NoDEA. Nonlinear Differential Equations and Applications 1 Taiwanese Journal of Mathematics 1 Journal of Inequalities and Applications 1 Annals of Mathematics. Second Series 1 Journal of the European Mathematical Society (JEMS) 1 Journal of Dynamical and Control Systems 1 Advanced Nonlinear Studies 1 Fixed Point Theory and Applications 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Bulletin of the American Mathematical Society 1 Journal of Fixed Point Theory and Applications 1 Journal of Modern Dynamics 1 Electronic Research Announcements in Mathematical Sciences 1 Analysis & PDE 1 Journal of Singularities ...and 6 more Serials all top 5 Cited in 34 Fields 241 Dynamical systems and ergodic theory (37-XX) 123 Mechanics of particles and systems (70-XX) 66 Ordinary differential equations (34-XX) 30 Partial differential equations (35-XX) 17 Several complex variables and analytic spaces (32-XX) 14 Quantum theory (81-XX) 13 Differential geometry (53-XX) 11 Global analysis, analysis on manifolds (58-XX) 10 Functions of a complex variable (30-XX) 10 Fluid mechanics (76-XX) 9 Numerical analysis (65-XX) 8 Operator theory (47-XX) 6 Manifolds and cell complexes (57-XX) 5 Number theory (11-XX) 4 Algebraic geometry (14-XX) 4 Computer science (68-XX) 3 Difference and functional equations (39-XX) 2 Measure and integration (28-XX) 2 Probability theory and stochastic processes (60-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Relativity and gravitational theory (83-XX) 1 General and overarching topics; collections (00-XX) 1 Real functions (26-XX) 1 Special functions (33-XX) 1 Sequences, series, summability (40-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Statistics (62-XX) 1 Mechanics of deformable solids (74-XX) 1 Geophysics (86-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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