Edit Profile (opens in new tab) Crauel, Hans Compute Distance To: Compute Author ID: crauel.hans Published as: Crauel, Hans; Crauel, H. Documents Indexed: 35 Publications since 1983, including 2 Books 3 Contributions as Editor Reviewing Activity: 276 Reviews Co-Authors: 24 Co-Authors with 23 Joint Publications 888 Co-Co-Authors all top 5 Co-Authors 15 single-authored 5 Flandoli, Franco 4 Arnold, Ludwig 3 Kloeden, Peter Eris 2 Imkeller, Peter 2 Scheutzow, Michael K. R. 2 Siegmund, Stefan 1 Bogenschütz, Thomas 1 Caraballo Garrido, Tomás 1 Damm, Tobias 1 Debussche, Arnaud 1 Dimitrov, Georgi K. 1 Doan, Thai Son 1 Duc, Luu Hoang 1 Eckmann, Jean-Pierre 1 Gundlach, Volker Matthias 1 Ilchmann, Achim 1 Langa, Jose’ Antonio 1 Matsikis, Iakovos 1 Real Anguas, José 1 Robinson, James Cooper 1 Steinkamp, Marcus 1 Townley, Stuart B. 1 Wihstutz, Volker 1 Yang, Meihua all top 5 Serials 5 Journal of Dynamics and Differential Equations 4 Stochastics and Dynamics 3 Archiv der Mathematik 2 Journal of Differential Equations 2 SIAM Journal on Control and Optimization 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Stochastics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Journal of the London Mathematical Society. Second Series 1 Proceedings of the American Mathematical Society 1 Probability Theory and Related Fields 1 Stochastic Processes and their Applications 1 Stochastics and Stochastics Reports 1 Journal of Difference Equations and Applications 1 Dynamical Systems 1 Lecture Notes in Mathematics 1 Boletín de la Sociedad Española de Matemática Aplicada. S\(\vec{\text{e}}\)MA all top 5 Fields 24 Dynamical systems and ergodic theory (37-XX) 23 Probability theory and stochastic processes (60-XX) 8 Ordinary differential equations (34-XX) 7 Partial differential equations (35-XX) 6 Systems theory; control (93-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 General and overarching topics; collections (00-XX) 3 Measure and integration (28-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 36 Publications have been cited 1,584 times in 923 Documents Cited by ▼ Year ▼ Attractors for random dynamical systems. Zbl 0819.58023Crauel, Hans; Flandoli, Franco 458 1994 Random attractors. Zbl 0884.58064Crauel, Hans; Debussche, Arnaud; Flandoli, Franco 448 1997 Stabilization of linear systems by noise. Zbl 0514.93069Arnold, Ludwig; Crauel, Hans; Wihstutz, Volker 88 1983 Random probability measures on Polish spaces. Zbl 1031.60041Crauel, Hans 84 2002 Random point attractors versus random set attractors. Zbl 1011.37032Crauel, Hans 59 2001 Global random attractors are uniquely determined by attracting deterministic compact sets. Zbl 0954.37027Crauel, Hans 50 1999 Additive noise destroys a pitchfork bifurcation. Zbl 0907.34042Crauel, Hans; Flandoli, Franco 48 1998 Hausdorff dimension of invariant sets for random dynamical systems. Zbl 0927.37031Crauel, Hans; Flandoli, Franco 37 1998 Random attractors of stochastic reaction-diffusion equations on variable domains. Zbl 1235.60076Crauel, H.; Kloeden, P. E.; Yang, Meihua 30 2011 Extremal exponents of random dynamical systems do not vanish. Zbl 0741.34026Crauel, Hans 26 1990 Markov measures for random dynamical systems. Zbl 0739.60066Crauel, Hans 26 1991 Nonautonomous and random attractors. Zbl 1358.37041Crauel, Hans; Kloeden, Peter E. 26 2015 Random dynamical systems. Zbl 0736.58029Arnold, Ludwig; Crauel, Hans 23 1991 The effect of noise on the Chafee-Infante equation: a nonlinear case study. Zbl 1173.60022Caraballo, Tomás; Crauel, Hans; Langa, José A.; Robinson, James C. 23 2007 Criteria for strong and weak random attractors. Zbl 1181.37075Crauel, Hans; Dimitroff, Georgi; Scheutzow, Michael 17 2009 Iterated function systems and multiplicative ergodic theory. Zbl 0760.60008Arnold, Ludwig; Crauel, Hans 15 1992 Bifurcations of one-dimensional stochastic differential equations. Zbl 0949.60066Crauel, Hans; Imkeller, Peter; Steinkamp, Marcus 14 1999 Towards a Morse theory for random dynamical systems. Zbl 1050.37026Crauel, Hans; Duc, Luu Hoang; Siegmund, Stefan 11 2004 Measure attractors and Markov attractors. Zbl 1153.37391Crauel, H. 11 2008 Minimal random attractors. Zbl 1386.37050Crauel, Hans; Scheutzow, Michael 9 2018 The Abramov-Rokhlin formula. Zbl 0764.58017Bogenschütz, Thomas; Crauel, Hans 9 1992 A uniformly exponential random forward attractor which is not a pullback attractor. Zbl 1015.37041Crauel, Hans 9 2002 Random dynamical systems: Positivity of Lyapunov exponents, and Markov systems. Zbl 0684.58019Crauel, Hans 8 1987 Stochastic partial differential equations with additive noise on time-varying domains. Zbl 1242.60063Crauel, Hans; Kloeden, Peter E.; Real Anguas, José 7 2010 Lyapunov exponents and invariant measures of stochastic systems on manifolds. Zbl 0596.58044Crauel, Hans 6 1986 White noise eliminates instability. Zbl 0997.37021Crauel, Hans 6 2000 Lyapunov exponents. Proceedings of a conference, held in Oberwolfach, Germany, May 28-June 2, 1990. Zbl 0733.00015 5 1991 Stochastic dynamics. Conference on Random dynamical systems, Bremen, Germany, April 28 - May 2, 1997. Dedicated to Ludwig Arnold on the ocassion of his 60th birthday. Zbl 0916.00011 5 1999 Difference equations with random delay. Zbl 1171.37325Crauel, H.; Doan, T. S.; Siegmund, S. 4 2009 Lyapunov exponents of random dynamical systems on Grassmannians. Zbl 0754.58019Crauel, Hans 4 1991 Invariant measures for random dynamical systems on the circle. Zbl 1015.37040Crauel, Hans 4 2002 Non-Markovian invariant measures are hyperbolic. Zbl 0778.60030Crauel, Hans 4 1993 Lyapunov numbers of Markov solutions of linear stochastic systems. Zbl 0564.60058Crauel, Hans 3 1984 Stabilization of linear systems by rotation. Zbl 1124.34031Crauel, Hans; Damm, Tobias; Ilchmann, Achim 3 2007 Dissipativity of three-dimensional stochastic Navier-Stokes equation. Zbl 0831.58032Crauel, Hans; Flandoli, Franco 2 1995 Noise assisted high-gain stabilization: Almost surely or in second mean. Zbl 1049.93084Crauel, Hans; Matsikis, Iakovos; Townley, Stuart 2 2003 Minimal random attractors. Zbl 1386.37050Crauel, Hans; Scheutzow, Michael 9 2018 Nonautonomous and random attractors. Zbl 1358.37041Crauel, Hans; Kloeden, Peter E. 26 2015 Random attractors of stochastic reaction-diffusion equations on variable domains. Zbl 1235.60076Crauel, H.; Kloeden, P. E.; Yang, Meihua 30 2011 Stochastic partial differential equations with additive noise on time-varying domains. Zbl 1242.60063Crauel, Hans; Kloeden, Peter E.; Real Anguas, José 7 2010 Criteria for strong and weak random attractors. Zbl 1181.37075Crauel, Hans; Dimitroff, Georgi; Scheutzow, Michael 17 2009 Difference equations with random delay. Zbl 1171.37325Crauel, H.; Doan, T. S.; Siegmund, S. 4 2009 Measure attractors and Markov attractors. Zbl 1153.37391Crauel, H. 11 2008 The effect of noise on the Chafee-Infante equation: a nonlinear case study. Zbl 1173.60022Caraballo, Tomás; Crauel, Hans; Langa, José A.; Robinson, James C. 23 2007 Stabilization of linear systems by rotation. Zbl 1124.34031Crauel, Hans; Damm, Tobias; Ilchmann, Achim 3 2007 Towards a Morse theory for random dynamical systems. Zbl 1050.37026Crauel, Hans; Duc, Luu Hoang; Siegmund, Stefan 11 2004 Noise assisted high-gain stabilization: Almost surely or in second mean. Zbl 1049.93084Crauel, Hans; Matsikis, Iakovos; Townley, Stuart 2 2003 Random probability measures on Polish spaces. Zbl 1031.60041Crauel, Hans 84 2002 A uniformly exponential random forward attractor which is not a pullback attractor. Zbl 1015.37041Crauel, Hans 9 2002 Invariant measures for random dynamical systems on the circle. Zbl 1015.37040Crauel, Hans 4 2002 Random point attractors versus random set attractors. Zbl 1011.37032Crauel, Hans 59 2001 White noise eliminates instability. Zbl 0997.37021Crauel, Hans 6 2000 Global random attractors are uniquely determined by attracting deterministic compact sets. Zbl 0954.37027Crauel, Hans 50 1999 Bifurcations of one-dimensional stochastic differential equations. Zbl 0949.60066Crauel, Hans; Imkeller, Peter; Steinkamp, Marcus 14 1999 Stochastic dynamics. Conference on Random dynamical systems, Bremen, Germany, April 28 - May 2, 1997. Dedicated to Ludwig Arnold on the ocassion of his 60th birthday. Zbl 0916.00011 5 1999 Additive noise destroys a pitchfork bifurcation. Zbl 0907.34042Crauel, Hans; Flandoli, Franco 48 1998 Hausdorff dimension of invariant sets for random dynamical systems. Zbl 0927.37031Crauel, Hans; Flandoli, Franco 37 1998 Random attractors. Zbl 0884.58064Crauel, Hans; Debussche, Arnaud; Flandoli, Franco 448 1997 Dissipativity of three-dimensional stochastic Navier-Stokes equation. Zbl 0831.58032Crauel, Hans; Flandoli, Franco 2 1995 Attractors for random dynamical systems. Zbl 0819.58023Crauel, Hans; Flandoli, Franco 458 1994 Non-Markovian invariant measures are hyperbolic. Zbl 0778.60030Crauel, Hans 4 1993 Iterated function systems and multiplicative ergodic theory. Zbl 0760.60008Arnold, Ludwig; Crauel, Hans 15 1992 The Abramov-Rokhlin formula. Zbl 0764.58017Bogenschütz, Thomas; Crauel, Hans 9 1992 Markov measures for random dynamical systems. Zbl 0739.60066Crauel, Hans 26 1991 Random dynamical systems. Zbl 0736.58029Arnold, Ludwig; Crauel, Hans 23 1991 Lyapunov exponents. Proceedings of a conference, held in Oberwolfach, Germany, May 28-June 2, 1990. Zbl 0733.00015 5 1991 Lyapunov exponents of random dynamical systems on Grassmannians. Zbl 0754.58019Crauel, Hans 4 1991 Extremal exponents of random dynamical systems do not vanish. Zbl 0741.34026Crauel, Hans 26 1990 Random dynamical systems: Positivity of Lyapunov exponents, and Markov systems. Zbl 0684.58019Crauel, Hans 8 1987 Lyapunov exponents and invariant measures of stochastic systems on manifolds. Zbl 0596.58044Crauel, Hans 6 1986 Lyapunov numbers of Markov solutions of linear stochastic systems. Zbl 0564.60058Crauel, Hans 3 1984 Stabilization of linear systems by noise. Zbl 0514.93069Arnold, Ludwig; Crauel, Hans; Wihstutz, Volker 88 1983 all cited Publications top 5 cited Publications all top 5 Cited by 874 Authors 49 Caraballo Garrido, Tomás 42 Wang, Bixiang 31 Langa, Jose’ Antonio 30 Kloeden, Peter Eris 30 Zhou, Shengfan 29 Li, Yangrong 20 Duan, Jinqiao 20 Guo, Boling 20 Real Anguas, José 19 Shu, Ji 19 Zhao, Wenqiang 18 Mao, Xuerong 18 Robinson, James Cooper 16 Scheutzow, Michael K. R. 15 Crauel, Hans 15 Gu, Anhui 15 Marín-Rubio, Pedro 14 Flandoli, Franco 14 Lu, Kening 13 Cui, Hongyong 13 Schmalfuß, Björn 12 Han, Xiaoying 12 Li, Dingshi 12 Valero, José 12 Wang, Zhaojuan 11 Gess, Benjamin 11 Huang, Jianhua 11 Wang, Xiaohu 10 Anguiano, María 10 Guo, Chunxiao 10 Wang, Renhai 9 Guo, Yanfeng 9 Li, Desheng 9 Ma, Qiaozhen 9 Yang, Meihua 9 You, Yuncheng 8 Gao, Hongjun 8 Kühn, Christian 8 Sun, Chunyou 8 Wang, Yejuan 8 Wu, Fuke 7 Barbu, Viorel 7 Ju, Xuewei 7 Łukaszewicz, Grzegorz 7 Nolasco de Carvalho, Alexandre 7 Shi, Lin 7 Tachim Medjo, Theodore 7 Wang, Wei 7 Xin, Jie 7 Zhang, Jian 7 Zhao, Caidi 6 Ding, Xiaoquan 6 Duc, Luu Hoang 6 Guzik, Grzegorz 6 Homburg, Ale Jan 6 Liang, Fei 6 Lv, Yan 6 Rasmussen, Martin 6 Rodkina, Alexandra 6 Urbański, Mariusz 6 You, Bo 6 Zhang, Yijin 5 Arnold, Ludwig 5 Bates, Peter W. 5 Blömker, Dirk 5 Chekroun, Mickaël D. 5 Da Prato, Giuseppe 5 Debussche, Arnaud 5 Deng, Feiqi 5 Engel, Maximilian 5 Garrido-Atienza, María José 5 Lawley, Sean D. 5 Li, Donglong 5 Li, Fang 5 Liu, Linfang 5 Neamţu, Alexandra 5 Park, Jong Yeoul 5 Röckner, Michael 5 Shen, Wenxian 5 Tan, Wen 4 Appleby, John A. D. 4 Brzeźniak, Zdzisław 4 Chen, Ercai 4 Chueshov, Igor’ Dmitrievich 4 Colucci, Renato 4 Doan, Thai Son 4 Friston, Karl J. 4 Ghil, Michael 4 Han, Yongqian 4 Herrera-Cobos, Marta 4 Hu, Shigeng 4 Huang, Xin 4 Jia, Xiaoyao 4 Jiang, Jifa 4 Lamb, Jeroen S. W. 4 Li, Jia 4 Li, Zhiming 4 Liu, Zhenxin 4 Lu, Hong 4 Nguyen Dinh Cong ...and 774 more Authors all top 5 Cited in 192 Serials 71 Journal of Differential Equations 57 Discrete and Continuous Dynamical Systems. Series B 55 Stochastics and Dynamics 42 Journal of Mathematical Analysis and Applications 41 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 32 Stochastic Analysis and Applications 25 Journal of Mathematical Physics 25 Journal of Dynamics and Differential Equations 23 Physica D 23 Discrete and Continuous Dynamical Systems 20 Stochastic Processes and their Applications 18 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 17 Communications on Pure and Applied Analysis 15 Journal of Difference Equations and Applications 14 Dynamical Systems 13 Nonlinear Analysis. Real World Applications 12 Systems & Control Letters 12 Abstract and Applied Analysis 11 Applied Mathematics and Computation 11 Advances in Difference Equations 10 Nonlinearity 9 Ergodic Theory and Dynamical Systems 9 Boundary Value Problems 8 Communications in Mathematical Physics 8 Probability Theory and Related Fields 7 Computers & Mathematics with Applications 7 Transactions of the American Mathematical Society 6 International Journal of Control 6 Journal of Statistical Physics 6 Proceedings of the American Mathematical Society 5 Applicable Analysis 5 Journal of Mathematical Biology 5 Chaos, Solitons and Fractals 5 The Annals of Probability 5 SIAM Journal on Control and Optimization 5 Nonlinear Dynamics 5 SIAM Journal on Applied Dynamical Systems 5 Journal of Applied Analysis and Computation 4 Applied Mathematics and Optimization 4 Journal of Functional Analysis 4 Applied Mathematics and Mechanics. (English Edition) 4 Communications in Partial Differential Equations 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 NoDEA. Nonlinear Differential Equations and Applications 4 Mathematical Problems in Engineering 4 Journal of Inequalities and Applications 4 Chaos 4 Discrete Dynamics in Nature and Society 4 Stochastics 4 Electronic Journal of Statistics 4 Discrete and Continuous Dynamical Systems. Series S 4 Open Mathematics 4 Electronic Research Archive 3 Journal of the Franklin Institute 3 Mathematical Methods in the Applied Sciences 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Automatica 3 Statistics & Probability Letters 3 Acta Mathematicae Applicatae Sinica. English Series 3 Science in China. Series A 3 The Annals of Applied Probability 3 Journal of Nonlinear Science 3 Taiwanese Journal of Mathematics 3 Qualitative Theory of Dynamical Systems 3 Differential Equations 3 Frontiers of Mathematics in China 3 AIMS Mathematics 2 Acta Mechanica 2 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 2 Journal d’Analyse Mathématique 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Advances in Mathematics 2 Archiv der Mathematik 2 Monatshefte für Mathematik 2 Results in Mathematics 2 Chinese Annals of Mathematics. Series B 2 Dynamics and Stability of Systems 2 MCSS. Mathematics of Control, Signals, and Systems 2 Neural Computation 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 SIAM Journal on Mathematical Analysis 2 Indagationes Mathematicae. New Series 2 Vestnik St. Petersburg University. Mathematics 2 Bulletin des Sciences Mathématiques 2 Complexity 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Infinite Dimensional Analysis, Quantum Probability and Related Topics 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Journal of Mathematical Fluid Mechanics 2 Acta Mathematica Sinica. English Series 2 Communications in Nonlinear Science and Numerical Simulation 2 Journal of Dynamical and Control Systems 2 Journal of Evolution Equations 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Acta Mechanica Sinica 2 Set-Valued and Variational Analysis 2 Science China. Mathematics 2 Mathematical Control and Related Fields 2 Stochastic and Partial Differential Equations. Analysis and Computations 2 Evolution Equations and Control Theory ...and 92 more Serials all top 5 Cited in 37 Fields 551 Dynamical systems and ergodic theory (37-XX) 450 Partial differential equations (35-XX) 443 Probability theory and stochastic processes (60-XX) 140 Ordinary differential equations (34-XX) 84 Systems theory; control (93-XX) 68 Fluid mechanics (76-XX) 52 Biology and other natural sciences (92-XX) 22 Operator theory (47-XX) 21 Measure and integration (28-XX) 21 Geophysics (86-XX) 20 Numerical analysis (65-XX) 17 Mechanics of deformable solids (74-XX) 13 Difference and functional equations (39-XX) 11 Real functions (26-XX) 10 Statistical mechanics, structure of matter (82-XX) 9 Statistics (62-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 General topology (54-XX) 7 Global analysis, analysis on manifolds (58-XX) 5 Integral equations (45-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Mechanics of particles and systems (70-XX) 3 Functional analysis (46-XX) 3 Computer science (68-XX) 3 Quantum theory (81-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Functions of a complex variable (30-XX) 2 Differential geometry (53-XX) 2 Information and communication theory, circuits (94-XX) 1 Number theory (11-XX) 1 Topological groups, Lie groups (22-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Abstract harmonic analysis (43-XX) 1 Manifolds and cell complexes (57-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Relativity and gravitational theory (83-XX) Citations by Year