Edit Profile (opens in new tab) Crauel, Hans Co-Author Distance 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 953 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 1,797 times in 1,047 Documents Cited by ▼ Year ▼ Attractors for random dynamical systems. Zbl 0819.58023Crauel, Hans; Flandoli, Franco 516 1994 Random attractors. Zbl 0884.58064Crauel, Hans; Debussche, Arnaud; Flandoli, Franco 503 1997 Random probability measures on Polish spaces. Zbl 1031.60041Crauel, Hans 106 2002 Stabilization of linear systems by noise. Zbl 0514.93069Arnold, Ludwig; Crauel, Hans; Wihstutz, Volker 94 1983 Random point attractors versus random set attractors. Zbl 1011.37032Crauel, Hans 62 2001 Additive noise destroys a pitchfork bifurcation. Zbl 0907.34042Crauel, Hans; Flandoli, Franco 61 1998 Global random attractors are uniquely determined by attracting deterministic compact sets. Zbl 0954.37027Crauel, Hans 58 1999 Hausdorff dimension of invariant sets for random dynamical systems. Zbl 0927.37031Crauel, Hans; Flandoli, Franco 41 1998 Random attractors of stochastic reaction-diffusion equations on variable domains. Zbl 1235.60076Crauel, H.; Kloeden, P. E.; Yang, Meihua 35 2011 Markov measures for random dynamical systems. Zbl 0739.60066Crauel, Hans 31 1991 Extremal exponents of random dynamical systems do not vanish. Zbl 0741.34026Crauel, Hans 31 1990 Nonautonomous and random attractors. Zbl 1358.37041Crauel, Hans; Kloeden, Peter E. 30 2015 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. 28 2007 Random dynamical systems. Zbl 0736.58029Arnold, Ludwig; Crauel, Hans 25 1991 Criteria for strong and weak random attractors. Zbl 1181.37075Crauel, Hans; Dimitroff, Georgi; Scheutzow, Michael 18 2009 The Abramov-Rokhlin formula. Zbl 0764.58017Bogenschütz, Thomas; Crauel, Hans 17 1992 Bifurcations of one-dimensional stochastic differential equations. Zbl 0949.60066Crauel, Hans; Imkeller, Peter; Steinkamp, Marcus 16 1999 Iterated function systems and multiplicative ergodic theory. Zbl 0760.60008Arnold, Ludwig; Crauel, Hans 15 1992 Towards a Morse theory for random dynamical systems. Zbl 1050.37026Crauel, Hans; Duc, Luu Hoang; Siegmund, Stefan 12 2004 Measure attractors and Markov attractors. Zbl 1153.37391Crauel, H. 11 2008 Minimal random attractors. Zbl 1386.37050Crauel, Hans; Scheutzow, Michael 9 2018 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 8 2010 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 7 1999 Lyapunov exponents. Proceedings of a conference, held in Oberwolfach, Germany, May 28-June 2, 1990. Zbl 0733.00015 6 1991 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 Non-Markovian invariant measures are hyperbolic. Zbl 0778.60030Crauel, Hans 5 1993 Lyapunov exponents of random dynamical systems on Grassmannians. Zbl 0754.58019Crauel, Hans 5 1991 Invariant measures for random dynamical systems on the circle. Zbl 1015.37040Crauel, Hans 4 2002 Difference equations with random delay. Zbl 1171.37325Crauel, H.; Doan, T. S.; Siegmund, S. 4 2009 Stabilization of linear systems by rotation. Zbl 1124.34031Crauel, Hans; Damm, Tobias; Ilchmann, Achim 3 2007 Lyapunov numbers of Markov solutions of linear stochastic systems. Zbl 0564.60058Crauel, Hans 3 1984 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. 30 2015 Random attractors of stochastic reaction-diffusion equations on variable domains. Zbl 1235.60076Crauel, H.; Kloeden, P. E.; Yang, Meihua 35 2011 Stochastic partial differential equations with additive noise on time-varying domains. Zbl 1242.60063Crauel, Hans; Kloeden, Peter E.; Real Anguas, José 8 2010 Criteria for strong and weak random attractors. Zbl 1181.37075Crauel, Hans; Dimitroff, Georgi; Scheutzow, Michael 18 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. 28 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 12 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 106 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 62 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 58 1999 Bifurcations of one-dimensional stochastic differential equations. Zbl 0949.60066Crauel, Hans; Imkeller, Peter; Steinkamp, Marcus 16 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 7 1999 Additive noise destroys a pitchfork bifurcation. Zbl 0907.34042Crauel, Hans; Flandoli, Franco 61 1998 Hausdorff dimension of invariant sets for random dynamical systems. Zbl 0927.37031Crauel, Hans; Flandoli, Franco 41 1998 Random attractors. Zbl 0884.58064Crauel, Hans; Debussche, Arnaud; Flandoli, Franco 503 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 516 1994 Non-Markovian invariant measures are hyperbolic. Zbl 0778.60030Crauel, Hans 5 1993 The Abramov-Rokhlin formula. Zbl 0764.58017Bogenschütz, Thomas; Crauel, Hans 17 1992 Iterated function systems and multiplicative ergodic theory. Zbl 0760.60008Arnold, Ludwig; Crauel, Hans 15 1992 Markov measures for random dynamical systems. Zbl 0739.60066Crauel, Hans 31 1991 Random dynamical systems. Zbl 0736.58029Arnold, Ludwig; Crauel, Hans 25 1991 Lyapunov exponents. Proceedings of a conference, held in Oberwolfach, Germany, May 28-June 2, 1990. Zbl 0733.00015 6 1991 Lyapunov exponents of random dynamical systems on Grassmannians. Zbl 0754.58019Crauel, Hans 5 1991 Extremal exponents of random dynamical systems do not vanish. Zbl 0741.34026Crauel, Hans 31 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 94 1983 all cited Publications top 5 cited Publications all top 5 Cited by 1,001 Authors 54 Caraballo Garrido, Tomás 46 Wang, Bixiang 35 Li, Yangrong 32 Kloeden, Peter Eris 32 Langa, Jose’ Antonio 30 Zhou, Shengfan 23 Shu, Ji 23 Zhao, Wenqiang 21 Duan, Jinqiao 20 Guo, Boling 20 Real Anguas, José 19 Mao, Xuerong 18 Robinson, James Cooper 17 Gu, Anhui 16 Flandoli, Franco 16 Marín-Rubio, Pedro 16 Scheutzow, Michael K. R. 15 Crauel, Hans 14 Cui, Hongyong 14 Huang, Jianhua 14 Lu, Kening 13 Han, Xiaoying 13 Li, Dingshi 13 Schmalfuß, Björn 13 Valero, José 13 Wang, Renhai 12 Wang, Zhaojuan 11 Gess, Benjamin 11 Guo, Chunxiao 11 Guo, Yanfeng 11 Ma, Qiaozhen 11 Wang, Xiaohu 10 Anguiano, María 10 Wang, Yejuan 9 Li, Desheng 9 Yang, Meihua 9 You, Yuncheng 9 Zhang, Jian 8 Gao, Hongjun 8 Kühn, Christian 8 Nolasco de Carvalho, Alexandre 8 Sun, Chunyou 8 Wu, Fuke 8 Xin, Jie 7 Barbu, Viorel 7 Duc, Luu Hoang 7 Engel, Maximilian 7 Ju, Xuewei 7 Kinra, Kush 7 Łukaszewicz, Grzegorz 7 Mohan, Manil Thankamani 7 Neamţu, Alexandra 7 Rasmussen, Martin 7 Shi, Lin 7 Wang, Wei 7 You, Bo 7 Zhang, Qiangheng 7 Zhang, Yijin 7 Zhao, Caidi 6 Blömker, Dirk 6 Chekroun, Mickaël D. 6 Chen, Ercai 6 Debussche, Arnaud 6 Ding, Xiaoquan 6 Guzik, Grzegorz 6 Homburg, Ale Jan 6 Huang, Xin 6 Jiang, Jifa 6 Li, Donglong 6 Li, Fang 6 Liang, Fei 6 Lv, Yan 6 Rodkina, Alexandra 6 Urbański, Mariusz 6 Xu, Ling 6 Yang, Shuang 6 Yao, Xiaobin 5 Arnold, Ludwig 5 Bates, Peter W. 5 Chen, Pengyu 5 Da Prato, Giuseppe 5 Deng, Feiqi 5 Doan, Thai Son 5 Friston, Karl J. 5 Garrido-Atienza, María José 5 Gelfert, Katrin Grit 5 Lamb, Jeroen S. W. 5 Lawley, Sean D. 5 Liu, Hui 5 Liu, Linfang 5 Lu, Hong 5 Park, Jong Yeoul 5 Röckner, Michael 5 Shen, Wenxian 5 Tan, Wen 5 Xu, Wei 5 Zhu, Quanxin 4 Appleby, John A. D. 4 Brzeźniak, Zdzisław 4 Cao, Dengqing ...and 901 more Authors all top 5 Cited in 211 Serials 78 Journal of Differential Equations 70 Discrete and Continuous Dynamical Systems. Series B 64 Stochastics and Dynamics 42 Journal of Mathematical Analysis and Applications 41 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 35 Stochastic Analysis and Applications 30 Journal of Mathematical Physics 27 Journal of Dynamics and Differential Equations 25 Discrete and Continuous Dynamical Systems 24 Physica D 20 Stochastic Processes and their Applications 19 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 18 Communications on Pure and Applied Analysis 15 Journal of Difference Equations and Applications 14 Dynamical Systems 13 Nonlinear Analysis. Real World Applications 13 Advances in Difference Equations 12 Nonlinearity 12 Systems & Control Letters 12 Abstract and Applied Analysis 11 Applied Mathematics and Computation 11 Ergodic Theory and Dynamical Systems 10 Probability Theory and Related Fields 9 Communications in Mathematical Physics 9 Boundary Value Problems 8 Transactions of the American Mathematical Society 8 SIAM Journal on Applied Dynamical Systems 8 Stochastics 7 Computers & Mathematics with Applications 7 International Journal of Control 7 Chaos, Solitons and Fractals 7 SIAM Journal on Control and Optimization 7 Discrete and Continuous Dynamical Systems. Series S 6 Applicable Analysis 6 Journal of Statistical Physics 6 Proceedings of the American Mathematical Society 6 Communications in Nonlinear Science and Numerical Simulation 5 Journal of Mathematical Biology 5 The Annals of Probability 5 Applied Mathematics and Optimization 5 Automatica 5 SIAM Journal on Mathematical Analysis 5 Nonlinear Dynamics 5 Journal of Applied Analysis and Computation 5 Evolution Equations and Control Theory 5 Open Mathematics 5 AIMS Mathematics 4 Journal of the Franklin Institute 4 Journal of Functional Analysis 4 Applied Mathematics and Mechanics. (English Edition) 4 The Annals of Applied Probability 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 Electronic Journal of Statistics 4 Banach Journal of Mathematical Analysis 4 Electronic Research Archive 3 Mathematical Methods in the Applied Sciences 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Statistics & Probability Letters 3 Acta Mathematicae Applicatae Sinica. English Series 3 Science in China. Series A 3 Journal of Nonlinear Science 3 Bulletin des Sciences Mathématiques 3 Taiwanese Journal of Mathematics 3 Qualitative Theory of Dynamical Systems 3 Differential Equations 3 Journal of Evolution Equations 3 Frontiers of Mathematics in China 3 Science China. 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 SIAM Journal on Numerical Analysis 2 Chinese Annals of Mathematics. Series B 2 Applied Mathematics Letters 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 Indagationes Mathematicae. New Series 2 Vestnik St. Petersburg University. Mathematics 2 Topological Methods in Nonlinear Analysis 2 Complexity 2 Electronic Journal of Probability 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 Journal of Dynamical and Control Systems ...and 111 more Serials all top 5 Cited in 37 Fields 634 Dynamical systems and ergodic theory (37-XX) 519 Partial differential equations (35-XX) 501 Probability theory and stochastic processes (60-XX) 154 Ordinary differential equations (34-XX) 92 Systems theory; control (93-XX) 77 Fluid mechanics (76-XX) 57 Biology and other natural sciences (92-XX) 29 Measure and integration (28-XX) 23 Operator theory (47-XX) 23 Numerical analysis (65-XX) 23 Geophysics (86-XX) 19 Mechanics of deformable solids (74-XX) 14 Real functions (26-XX) 14 Difference and functional equations (39-XX) 11 Statistical mechanics, structure of matter (82-XX) 11 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Statistics (62-XX) 8 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) 4 Functional analysis (46-XX) 4 Computer science (68-XX) 3 Topological groups, Lie groups (22-XX) 3 Quantum theory (81-XX) 2 Number theory (11-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Functions of a complex variable (30-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Differential geometry (53-XX) 2 Manifolds and cell complexes (57-XX) 2 Information and communication theory, circuits (94-XX) 1 Special functions (33-XX) 1 Abstract harmonic analysis (43-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Relativity and gravitational theory (83-XX) Citations by Year