## Crauel, Hans

Compute Distance To:
 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
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### 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
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### 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
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### 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)

### 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 0819.58023
Crauel, Hans; Flandoli, Franco
1994
Random attractors. Zbl 0884.58064
Crauel, Hans; Debussche, Arnaud; Flandoli, Franco
1997
Stabilization of linear systems by noise. Zbl 0514.93069
Arnold, Ludwig; Crauel, Hans; Wihstutz, Volker
1983
Random probability measures on Polish spaces. Zbl 1031.60041
Crauel, Hans
2002
Random point attractors versus random set attractors. Zbl 1011.37032
Crauel, Hans
2001
Global random attractors are uniquely determined by attracting deterministic compact sets. Zbl 0954.37027
Crauel, Hans
1999
Additive noise destroys a pitchfork bifurcation. Zbl 0907.34042
Crauel, Hans; Flandoli, Franco
1998
Hausdorff dimension of invariant sets for random dynamical systems. Zbl 0927.37031
Crauel, Hans; Flandoli, Franco
1998
Random attractors of stochastic reaction-diffusion equations on variable domains. Zbl 1235.60076
Crauel, H.; Kloeden, P. E.; Yang, Meihua
2011
Extremal exponents of random dynamical systems do not vanish. Zbl 0741.34026
Crauel, Hans
1990
Markov measures for random dynamical systems. Zbl 0739.60066
Crauel, Hans
1991
Nonautonomous and random attractors. Zbl 1358.37041
Crauel, Hans; Kloeden, Peter E.
2015
Random dynamical systems. Zbl 0736.58029
Arnold, Ludwig; Crauel, Hans
1991
The effect of noise on the Chafee-Infante equation: a nonlinear case study. Zbl 1173.60022
Caraballo, Tomás; Crauel, Hans; Langa, José A.; Robinson, James C.
2007
Criteria for strong and weak random attractors. Zbl 1181.37075
Crauel, Hans; Dimitroff, Georgi; Scheutzow, Michael
2009
Iterated function systems and multiplicative ergodic theory. Zbl 0760.60008
Arnold, Ludwig; Crauel, Hans
1992
Bifurcations of one-dimensional stochastic differential equations. Zbl 0949.60066
Crauel, Hans; Imkeller, Peter; Steinkamp, Marcus
1999
Towards a Morse theory for random dynamical systems. Zbl 1050.37026
Crauel, Hans; Duc, Luu Hoang; Siegmund, Stefan
2004
Measure attractors and Markov attractors. Zbl 1153.37391
Crauel, H.
2008
Minimal random attractors. Zbl 1386.37050
Crauel, Hans; Scheutzow, Michael
2018
The Abramov-Rokhlin formula. Zbl 0764.58017
Bogenschütz, Thomas; Crauel, Hans
1992
A uniformly exponential random forward attractor which is not a pullback attractor. Zbl 1015.37041
Crauel, Hans
2002
Random dynamical systems: Positivity of Lyapunov exponents, and Markov systems. Zbl 0684.58019
Crauel, Hans
1987
Stochastic partial differential equations with additive noise on time-varying domains. Zbl 1242.60063
Crauel, Hans; Kloeden, Peter E.; Real Anguas, José
2010
Lyapunov exponents and invariant measures of stochastic systems on manifolds. Zbl 0596.58044
Crauel, Hans
1986
White noise eliminates instability. Zbl 0997.37021
Crauel, Hans
2000
Lyapunov exponents. Proceedings of a conference, held in Oberwolfach, Germany, May 28-June 2, 1990. Zbl 0733.00015
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
1999
Difference equations with random delay. Zbl 1171.37325
Crauel, H.; Doan, T. S.; Siegmund, S.
2009
Lyapunov exponents of random dynamical systems on Grassmannians. Zbl 0754.58019
Crauel, Hans
1991
Invariant measures for random dynamical systems on the circle. Zbl 1015.37040
Crauel, Hans
2002
Non-Markovian invariant measures are hyperbolic. Zbl 0778.60030
Crauel, Hans
1993
Lyapunov numbers of Markov solutions of linear stochastic systems. Zbl 0564.60058
Crauel, Hans
1984
Stabilization of linear systems by rotation. Zbl 1124.34031
Crauel, Hans; Damm, Tobias; Ilchmann, Achim
2007
Dissipativity of three-dimensional stochastic Navier-Stokes equation. Zbl 0831.58032
Crauel, Hans; Flandoli, Franco
1995
Noise assisted high-gain stabilization: Almost surely or in second mean. Zbl 1049.93084
Crauel, Hans; Matsikis, Iakovos; Townley, Stuart
2003
Minimal random attractors. Zbl 1386.37050
Crauel, Hans; Scheutzow, Michael
2018
Nonautonomous and random attractors. Zbl 1358.37041
Crauel, Hans; Kloeden, Peter E.
2015
Random attractors of stochastic reaction-diffusion equations on variable domains. Zbl 1235.60076
Crauel, H.; Kloeden, P. E.; Yang, Meihua
2011
Stochastic partial differential equations with additive noise on time-varying domains. Zbl 1242.60063
Crauel, Hans; Kloeden, Peter E.; Real Anguas, José
2010
Criteria for strong and weak random attractors. Zbl 1181.37075
Crauel, Hans; Dimitroff, Georgi; Scheutzow, Michael
2009
Difference equations with random delay. Zbl 1171.37325
Crauel, H.; Doan, T. S.; Siegmund, S.
2009
Measure attractors and Markov attractors. Zbl 1153.37391
Crauel, H.
2008
The effect of noise on the Chafee-Infante equation: a nonlinear case study. Zbl 1173.60022
Caraballo, Tomás; Crauel, Hans; Langa, José A.; Robinson, James C.
2007
Stabilization of linear systems by rotation. Zbl 1124.34031
Crauel, Hans; Damm, Tobias; Ilchmann, Achim
2007
Towards a Morse theory for random dynamical systems. Zbl 1050.37026
Crauel, Hans; Duc, Luu Hoang; Siegmund, Stefan
2004
Noise assisted high-gain stabilization: Almost surely or in second mean. Zbl 1049.93084
Crauel, Hans; Matsikis, Iakovos; Townley, Stuart
2003
Random probability measures on Polish spaces. Zbl 1031.60041
Crauel, Hans
2002
A uniformly exponential random forward attractor which is not a pullback attractor. Zbl 1015.37041
Crauel, Hans
2002
Invariant measures for random dynamical systems on the circle. Zbl 1015.37040
Crauel, Hans
2002
Random point attractors versus random set attractors. Zbl 1011.37032
Crauel, Hans
2001
White noise eliminates instability. Zbl 0997.37021
Crauel, Hans
2000
Global random attractors are uniquely determined by attracting deterministic compact sets. Zbl 0954.37027
Crauel, Hans
1999
Bifurcations of one-dimensional stochastic differential equations. Zbl 0949.60066
Crauel, Hans; Imkeller, Peter; Steinkamp, Marcus
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
1999
Additive noise destroys a pitchfork bifurcation. Zbl 0907.34042
Crauel, Hans; Flandoli, Franco
1998
Hausdorff dimension of invariant sets for random dynamical systems. Zbl 0927.37031
Crauel, Hans; Flandoli, Franco
1998
Random attractors. Zbl 0884.58064
Crauel, Hans; Debussche, Arnaud; Flandoli, Franco
1997
Dissipativity of three-dimensional stochastic Navier-Stokes equation. Zbl 0831.58032
Crauel, Hans; Flandoli, Franco
1995
Attractors for random dynamical systems. Zbl 0819.58023
Crauel, Hans; Flandoli, Franco
1994
Non-Markovian invariant measures are hyperbolic. Zbl 0778.60030
Crauel, Hans
1993
Iterated function systems and multiplicative ergodic theory. Zbl 0760.60008
Arnold, Ludwig; Crauel, Hans
1992
The Abramov-Rokhlin formula. Zbl 0764.58017
Bogenschütz, Thomas; Crauel, Hans
1992
Markov measures for random dynamical systems. Zbl 0739.60066
Crauel, Hans
1991
Random dynamical systems. Zbl 0736.58029
Arnold, Ludwig; Crauel, Hans
1991
Lyapunov exponents. Proceedings of a conference, held in Oberwolfach, Germany, May 28-June 2, 1990. Zbl 0733.00015
1991
Lyapunov exponents of random dynamical systems on Grassmannians. Zbl 0754.58019
Crauel, Hans
1991
Extremal exponents of random dynamical systems do not vanish. Zbl 0741.34026
Crauel, Hans
1990
Random dynamical systems: Positivity of Lyapunov exponents, and Markov systems. Zbl 0684.58019
Crauel, Hans
1987
Lyapunov exponents and invariant measures of stochastic systems on manifolds. Zbl 0596.58044
Crauel, Hans
1986
Lyapunov numbers of Markov solutions of linear stochastic systems. Zbl 0564.60058
Crauel, Hans
1984
Stabilization of linear systems by noise. Zbl 0514.93069
Arnold, Ludwig; Crauel, Hans; Wihstutz, Volker
1983
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### 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
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### 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
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### 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)