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## Arnold, Ludwig

Compute Distance To:
 Author ID: arnold.ludwig Published as: Arnold, L.; Arnold, Ludwig External Links: MGP
 Documents Indexed: 100 Publications since 1963, including 7 Books Reviewing Activity: 31 Reviews Biographic References: 2 Publications
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#### Co-Authors

 35 single-authored 8 Wihstutz, Volker 7 Imkeller, Peter 5 Chueshov, Igor’ Dmitrievich 5 Nguyen Dinh Cong 4 Crauel, Hans 4 Kliemann, Wolfgang H. 4 Namachchivaya, N. Sri 4 Xu, Kedai 3 Boxler, Petra 2 Doyle, Monica M. 2 Gundlach, Volker Matthias 2 Kloeden, Peter Eris 2 Kotelenez, Peter M. 2 Michalicek, Johannes 2 Ochs, Gunter 2 Oeljeklaus, Eberhard 2 Oseledets, Valeriĭ Iustinovich 2 San Martin, Luiz Antonio Barrera 2 Schenk-Hoppé, Klaus Reiner 2 Schmalfuß, Björn 1 Bharucha-Reid, Albert Turner 1 Bleckert, Gabriele 1 Curtain, Ruth Frances 1 Demetrius, Lloyd A. 1 Eckmann, Jean-Pierre 1 Eizenberg, Alexander 1 Evstigneev, Igor V. 1 Horsthemke, Werner 1 Khas’minskiĭ, Rafail Zalmanovich 1 Lefever, René 1 Papanicolaou, George C. 1 Pardoux, Etienne 1 Resz, H. 1 Roos, Pontus 1 Scheutzow, Michael K. R. 1 Stuckl, J. W. 1 Theodosopulu, M. 1 Tudor, Constantin 1 Wu, Yonghui
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#### Serials

 4 Stochastics and Stochastics Reports 3 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 3 SIAM Journal on Applied Mathematics 2 Israel Journal of Mathematics 2 Stochastics 2 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 2 Journal of Differential Equations 2 Mathematische Zeitschrift 2 SIAM Journal on Control and Optimization 2 Ergodic Theory and Dynamical Systems 2 Probability Theory and Related Fields 2 Dynamics and Stability of Systems 2 Journal of Dynamics and Differential Equations 2 Random & Computational Dynamics 2 Random Operators and Stochastic Equations 2 Lecture Notes in Mathematics 1 Advances in Applied Probability 1 Bulletin of the Australian Mathematical Society 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Mathematical Analysis and Applications 1 Journal of Sound and Vibration 1 Zastosowania Matematyki 1 The Annals of Probability 1 Archiv der Mathematik 1 Biometrical Journal 1 Journal für die Reine und Angewandte Mathematik 1 Match 1 Mathematische Nachrichten 1 Transactions of the American Mathematical Society 1 The Annals of Applied Probability 1 Linear Algebra and its Applications 1 Stochastic Processes and their Applications 1 Matemática Aplicada e Computacional 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Computational and Applied Mathematics 1 Discrete and Continuous Dynamical Systems 1 Nonlinear Dynamics 1 Positivity 1 Dynamical Systems 1 Discrete and Continuous Dynamical Systems. Series B 1 Bulletin of the American Mathematical Society 1 Österreichische Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Klasse. Sitzungsberichte. Abteilung II 1 Springer Series in Synergetics 1 Springer Monographs in Mathematics
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#### Fields

 69 Probability theory and stochastic processes (60-XX) 36 Systems theory; control (93-XX) 35 Ordinary differential equations (34-XX) 28 Dynamical systems and ergodic theory (37-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 7 Mechanics of particles and systems (70-XX) 6 Measure and integration (28-XX) 4 General and overarching topics; collections (00-XX) 3 Operator theory (47-XX) 3 Biology and other natural sciences (92-XX) 2 Functional analysis (46-XX) 2 Fluid mechanics (76-XX) 2 Geophysics (86-XX) 1 History and biography (01-XX) 1 Topological groups, Lie groups (22-XX) 1 Partial differential equations (35-XX) 1 Integral equations (45-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Numerical analysis (65-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

#### Citations contained in zbMATH

90 Publications have been cited 2,332 times in 1,952 Documents Cited by Year
Random dynamical systems. Zbl 0906.34001
Arnold, Ludwig
1998
Stochastic differential equations: Theory and applications. Translation. Zbl 0278.60039
Arnold, Ludwig
1974
Stabilization of linear systems by noise. Zbl 0514.93069
Arnold, Ludwig; Crauel, Hans; Wihstutz, Volker
1983
The influence of external real and white noise on the Lotka-Volterra model. Zbl 0433.92019
Arnold, L.; Horsthemke, W.; Stuckl, J. W.
1979
A formula connecting sample and moment stability of linear stochastic systems. Zbl 0561.93063
Arnold, Ludwig
1984
Asymptotic analysis of the Lyapunov exponent and rotation number of the random oscillator and applications. Zbl 0603.60051
Arnold, Ludwig; Papanicolaou, George; Wihstutz, Volker
1986
On the asymptotic distribution of the eigenvalues of random matrices. Zbl 0246.60029
Arnold, Ludwig
1967
Evolutionary formalism for products of positive random matrices. Zbl 0818.15015
Arnold, Ludwig; Gundlach, Volker Matthias; Demetrius, Lloyd
1994
Order-preserving random dynamical systems: Equilibria, attractors, applications. Zbl 0938.37031
Arnold, Ludwig; Chueshov, Igor
1998
Toward an understanding of stochastic Hopf bifurcation: a case study. Zbl 1298.37038
Arnold, Ludwig; Namachchivaya, N. Sri; Schenk-Hoppé, Klaus R.
1996
Perfect cocycles through stochastic differential equations. Zbl 0821.60061
Arnold, Ludwig; Scheutzow, Michael
1995
Lyapunov exponents: A survey. Zbl 0599.60061
Arnold, Ludwig; Wihstutz, Volker
1986
Lyapunov exponents of linear stochastic systems. Zbl 0588.60047
Arnold, L.; Kliemann, W.; Oeljeklaus, Eberhard
1986
Stochastische Differentialgleichungen. Theorie und Anwendung. Zbl 0266.60039
Arnold, Ludwig
1973
Almost sure and moment stability for linear Ito equations. Zbl 0588.60049
Arnold, L.; Oeljeklaus, Eberhard; Pardoux, E.
1986
On unique ergodicity for degenerate diffusions. Zbl 0617.60076
Arnold, Ludwig; Kliemann, Wolfgang
1987
Stationary and almost periodic solutions of almost periodic affine stochastic differential equations. Zbl 1043.60513
Arnold, Ludwig; Tudor, Constantin
1998
Deterministic limit of the stochastic model of chemical reactions with diffusion. Zbl 0429.60025
Arnold, L.; Theodosopulu, M.
1980
On Wigner’s semicircle law for the eigenvalues of random matrices. Zbl 0212.51006
Arnold, L.
1971
Normal forms for stochastic differential equations. Zbl 0906.60048
Arnold, Ludwig; Imkeller, Peter
1998
Stabilization by noise revisited. Zbl 0765.93076
Arnold, L.
1990
Lyapunov’s second method for random dynamical systems. Zbl 1040.37035
Arnold, Ludwig; Schmalfuss, Björn
2001
Small noise expansion of moment Lyapunov exponents for two-dimensional systems. Zbl 0890.60055
Arnold, L.; Doyle, M. M.; Sri Namachchivaya, N.
1997
Random dynamical systems. Zbl 0736.58029
Arnold, Ludwig; Crauel, Hans
1991
Qualitative theory of stochastic systems. Zbl 0536.60070
Arnold, Ludwig; Kliemann, Wolfgang
1983
Random dynamical systems. Zbl 0834.58026
Arnold, Ludwig
1995
Iterated function systems and multiplicative ergodic theory. Zbl 0760.60008
Arnold, Ludwig; Crauel, Hans
1992
On Wigner’s semicircle law for the eigenvalues of random matrices. Zbl 0206.48202
Arnold, L.
1971
Hasselmann’s program revisited: The analysis of stochasticity in deterministic climate models. Zbl 1015.34037
Arnold, Ludwig
2001
Random dynamical systems. Zbl 0805.60048
Arnold, L.
1994
The stochastic Brusselator: Parametric noise destroys Hopf bifurcation. Zbl 0939.60057
Arnold, Ludwig; Bleckert, Gabriele; Schenk-Hoppé, Klaus Reiner
1999
Über die Konvergenz einer zufälligen Potenzreihe. Zbl 0146.38803
Arnold, Ludwig
1966
Stochastic nonlinear systems in physics, chemistry, and biology. Proceedings of the Workshop, Bielefeld, Fed. Rep. of Germany, October 5- 11, 1980. Zbl 0453.00034
Arnold, L. (ed.); Lefever, R. (ed.)
1981
Über die Nullstellenverteilung zufälliger Polynome. Zbl 0139.35801
Arnold, Ludwig
1966
Stability and capsizing of ships in random sea – a survey. Zbl 1090.70014
Arnold, Ludwig; Chueshov, Igor; Ochs, Gunter
2004
Stratonovich calculus with spatial parameters and anticipative problems in multiplicative ergodic theory. Zbl 0847.60037
Arnold, Ludwig; Imkeller, Peter
1996
Reduction of deterministic coupled atmosphere-ocean models to stochastic ocean models: a numerical case study of the Lorenz-Maas system. Zbl 1071.76045
Arnold, Ludwig; Imkeller, Peter; Wu, Yonghui
2003
Linear cocycles with simple Lyapunov spectrum are dense in $$L^\infty$$. Zbl 0952.37002
Arnold, Ludwig; Nguyen Dinh Cong
1999
Stochastic bifurcation: Instructive examples in dimension one. Zbl 0751.60057
Arnold, Ludwig; Boxler, Petra
1992
Large deviations of linear stochastic differential equations. Zbl 0632.60021
Arnold, Ludwig; Kliemann, Wolfgang
1987
The asymptotic stability of a noisy non-linear oscillator. Zbl 1236.70044
Arnold, L.; Imkeller, P.; Namachchivaya, N. Sri
2004
Cooperative random and stochastic differential equations. Zbl 1017.37026
Arnold, Ludwig; Chueshov, Igor
2001
Jordan normal form for linear cocycles. Zbl 0971.37002
Arnold, Ludwig; Nguyen Dinh Cong; Oseledets, Valery
1999
On the simplicity of the Lyapunov spectrum of products of random matrices. Zbl 0891.58022
Arnold, Ludwig; Cong, Nguyen Dinh
1997
Lyapunov exponents and rotation number of two-dimensional systems with telegraphic noise. Zbl 0684.60046
Arnold, Ludwig; Kloeden, Peter
1989
On the consistency of the mathematical models of chemical reactions. Zbl 0498.93052
Arnold, L.
1980
The log law for multidimensional stochastic integrals and diffusion processes. Zbl 0219.60047
Arnold, L.
1971
Convex-valued random dynamical systems: A variational principle for equilibrium states. Zbl 0933.93063
Arnold, L.; Evstigneev, I. V.; Gundlach, V. M.
1999
Lyapunov exponents. Proceedings of a conference, held in Oberwolfach, Germany, May 28-June 2, 1990. Zbl 0733.00015
Arnold, Ludwig (ed.); Crauel, Hans (ed.); Eckmann, Jean-Pierre (ed.)
1991
A multiplicative ergodic theorem for rotation numbers. Zbl 0684.34059
Arnold, Ludwig; San Martin, Luiz
1989
Lyapunov exponents. Proceedings of a Workshop held in Bremen, Germany, November 12-15, 1984. Zbl 0577.00017
Arnold, Ludwig (ed.); Wihstutz, Volker (ed.)
1986
Stochastic systems: qualitative theory and Lyapunov exponents. Zbl 0568.93068
Arnold, L.
1984
Fixed points and attractors for random dynamical systems. Zbl 0925.58050
Arnold, L.; Schmalfuss, B.
1996
Deterministic version of Wigner’s semicircle law for the distribution of matrix eigenvalues. Zbl 0332.15009
Arnold, Ludwig
1976
A limit set trichotomy for order-preserving random systems. Zbl 0997.34044
Arnold, Ludwig; Chueshov, Igor
2001
Stability index for nonlinear stochastic differential equations. Zbl 0827.93065
Arnold, Ludwig; Khasminskii, Rafail Z.
1995
Normal forms for random diffeomorphisms. Zbl 0763.34026
Arnold, Ludwig; Xu, Kedai
1992
A control problem related to the Lyapunov spectrum of stochastic flows. Zbl 0641.93069
San Martin, Luiz; Arnold, Ludwig
1986
Stationary solutions of linear systems with additive and multiplicative noise. Zbl 0479.60061
Arnold, Ludwig; Wihstutz, Volker
1982
Normal forms for random differential equations. Zbl 0820.34037
Arnold, Ludwig; Xu, Kedai
1995
Linear and nonlinear diffusion approximation of the slow motion in systems with two time scales. Zbl 1079.34046
Arnold, Ludwig
2003
Recent progress in stochastic bifurcation theory. Zbl 1226.70009
Arnold, Ludwig
2001
Rotation numbers for linear stochastic differential equations. Zbl 0944.60065
Arnold, Ludwig; Imkeller, Peter
1999
Trends and open problems in the theory of random dynamical systems. Zbl 1044.37516
Arnold, Ludwig
1998
Large noise asymptotics of invariant measures, with applications to Lyapunov exponents. Zbl 0869.93051
Arnold, Ludwig; Eizenberg, Alex; Wihstutz, Volker
1996
Discretization of a random dynamical system near a hyperbolic point. Zbl 0857.34058
Arnold, Ludwig; Kloeden, Peter
1996
Furstenberg-Khasminskii formulas for Lyapunov exponents via anticipative calculus. Zbl 0857.60052
Arnold, Ludwig; Imkeller, Peter
1995
Anticipative problems in the theory of random dynamical systems. Zbl 0821.60062
Arnold, Ludwig
1995
Generic properties of Lyapunov exponents. Zbl 0827.58030
Arnold, Ludwig; Nguyen Dinh Cong
1994
Simultaneous normal form and center manifold reduction for random differential equations. Zbl 0938.60512
Arnold, Ludwig; Xu, Kedai
1993
Additive noise turns a hyperbolic fixed point into a stationary solution. Zbl 0741.34010
Arnold, Ludwig; Boxler, Petra
1991
Stochastic differential equations as dynamical systems. Zbl 0727.93070
Arnold, Ludwig
1990
Eigenvalues, bifurcation, and center manifolds in the presence of noise. Zbl 0681.60055
Arnold, Ludwig; Boxler, Petra
1989
Linear stochastic evolution equation models for chemical reactions. Zbl 0461.60079
Arnold, Ludwig; Kotelenez, P.; Curtain, Ruth F.
1981
A new example of an unstable system being stabilized by random parameter noise. Zbl 0424.93059
Arnold, L.
1979
Complex-valued stable measures and their domains of attraction. Zbl 0174.19102
Arnold, Ludwig; Michaliček, Johannes
1969
Wachstumseigenschaften zufälliger ganzer Funktionen. Zbl 0203.17103
Arnold, Ludwig
1966
Numerische Experimente zur mehrdimensionalen Quadratur. Zbl 0128.36902
Roos, P.; Arnold, L.
1963
Random dynamical systems methods in ship stability: a case study. Zbl 1092.34028
Arnold, Ludwig; Chueshov, Igor; Ochs, Gunter
2005
On the integrability condition in the multiplicative ergodic theorem for stochastic differential equations. Zbl 1043.60512
Arnold, Ludwig; Imkeller, Peter
1998
Wide sense stationary solutions of linear systems with additive noise. Zbl 0517.93050
Arnold, Ludwig; Wihstutz, Volker
1983
The essential range of a nonabelian cocycle is not a cohomology invariant. Zbl 0989.37002
Arnold, L.; Nguyen Dinh Cong; Oseledets, V. I.
2000
The unfolding of dynamics in stochastic analysis. Zbl 0874.60048
Arnold, Ludwig
1997
Generation of random dynamical systems. Zbl 0864.60044
Arnold, Ludwig
1995
Invariant measures for random dynamical systems, and a necessary condition for stochastic bifurcation from a fixed point. Zbl 0807.58022
Arnold, Ludwig; Xu, Kedai
1994
Qualitative theory of stochastic non-linear systems. Zbl 0457.60037
Arnold, Ludwig
1981
On Fredholm integral equations with random degenerate kernels. Zbl 0224.60029
Bharucha-Reid, A. T.; Arnold, L.
1969
On the norm of stable measures. Zbl 0162.45301
Arnold, Ludwig; Michaliček, Johannes
1968
Konvergenzprobleme bei zufälligen Potenzreihen mit Lücken. Zbl 0146.38901
Arnold, Ludwig
1966
Digitale Simulation des Verkehrsablaufes auf einer Landstraße. Zbl 0122.13103
Arnold, L.; Resz, H.
1964
Random dynamical systems methods in ship stability: a case study. Zbl 1092.34028
Arnold, Ludwig; Chueshov, Igor; Ochs, Gunter
2005
Stability and capsizing of ships in random sea – a survey. Zbl 1090.70014
Arnold, Ludwig; Chueshov, Igor; Ochs, Gunter
2004
The asymptotic stability of a noisy non-linear oscillator. Zbl 1236.70044
Arnold, L.; Imkeller, P.; Namachchivaya, N. Sri
2004
Reduction of deterministic coupled atmosphere-ocean models to stochastic ocean models: a numerical case study of the Lorenz-Maas system. Zbl 1071.76045
Arnold, Ludwig; Imkeller, Peter; Wu, Yonghui
2003
Linear and nonlinear diffusion approximation of the slow motion in systems with two time scales. Zbl 1079.34046
Arnold, Ludwig
2003
Lyapunov’s second method for random dynamical systems. Zbl 1040.37035
Arnold, Ludwig; Schmalfuss, Björn
2001
Hasselmann’s program revisited: The analysis of stochasticity in deterministic climate models. Zbl 1015.34037
Arnold, Ludwig
2001
Cooperative random and stochastic differential equations. Zbl 1017.37026
Arnold, Ludwig; Chueshov, Igor
2001
A limit set trichotomy for order-preserving random systems. Zbl 0997.34044
Arnold, Ludwig; Chueshov, Igor
2001
Recent progress in stochastic bifurcation theory. Zbl 1226.70009
Arnold, Ludwig
2001
The essential range of a nonabelian cocycle is not a cohomology invariant. Zbl 0989.37002
Arnold, L.; Nguyen Dinh Cong; Oseledets, V. I.
2000
The stochastic Brusselator: Parametric noise destroys Hopf bifurcation. Zbl 0939.60057
Arnold, Ludwig; Bleckert, Gabriele; Schenk-Hoppé, Klaus Reiner
1999
Linear cocycles with simple Lyapunov spectrum are dense in $$L^\infty$$. Zbl 0952.37002
Arnold, Ludwig; Nguyen Dinh Cong
1999
Jordan normal form for linear cocycles. Zbl 0971.37002
Arnold, Ludwig; Nguyen Dinh Cong; Oseledets, Valery
1999
Convex-valued random dynamical systems: A variational principle for equilibrium states. Zbl 0933.93063
Arnold, L.; Evstigneev, I. V.; Gundlach, V. M.
1999
Rotation numbers for linear stochastic differential equations. Zbl 0944.60065
Arnold, Ludwig; Imkeller, Peter
1999
Random dynamical systems. Zbl 0906.34001
Arnold, Ludwig
1998
Order-preserving random dynamical systems: Equilibria, attractors, applications. Zbl 0938.37031
Arnold, Ludwig; Chueshov, Igor
1998
Stationary and almost periodic solutions of almost periodic affine stochastic differential equations. Zbl 1043.60513
Arnold, Ludwig; Tudor, Constantin
1998
Normal forms for stochastic differential equations. Zbl 0906.60048
Arnold, Ludwig; Imkeller, Peter
1998
Trends and open problems in the theory of random dynamical systems. Zbl 1044.37516
Arnold, Ludwig
1998
On the integrability condition in the multiplicative ergodic theorem for stochastic differential equations. Zbl 1043.60512
Arnold, Ludwig; Imkeller, Peter
1998
Small noise expansion of moment Lyapunov exponents for two-dimensional systems. Zbl 0890.60055
Arnold, L.; Doyle, M. M.; Sri Namachchivaya, N.
1997
On the simplicity of the Lyapunov spectrum of products of random matrices. Zbl 0891.58022
Arnold, Ludwig; Cong, Nguyen Dinh
1997
The unfolding of dynamics in stochastic analysis. Zbl 0874.60048
Arnold, Ludwig
1997
Toward an understanding of stochastic Hopf bifurcation: a case study. Zbl 1298.37038
Arnold, Ludwig; Namachchivaya, N. Sri; Schenk-Hoppé, Klaus R.
1996
Stratonovich calculus with spatial parameters and anticipative problems in multiplicative ergodic theory. Zbl 0847.60037
Arnold, Ludwig; Imkeller, Peter
1996
Fixed points and attractors for random dynamical systems. Zbl 0925.58050
Arnold, L.; Schmalfuss, B.
1996
Large noise asymptotics of invariant measures, with applications to Lyapunov exponents. Zbl 0869.93051
Arnold, Ludwig; Eizenberg, Alex; Wihstutz, Volker
1996
Discretization of a random dynamical system near a hyperbolic point. Zbl 0857.34058
Arnold, Ludwig; Kloeden, Peter
1996
Perfect cocycles through stochastic differential equations. Zbl 0821.60061
Arnold, Ludwig; Scheutzow, Michael
1995
Random dynamical systems. Zbl 0834.58026
Arnold, Ludwig
1995
Stability index for nonlinear stochastic differential equations. Zbl 0827.93065
Arnold, Ludwig; Khasminskii, Rafail Z.
1995
Normal forms for random differential equations. Zbl 0820.34037
Arnold, Ludwig; Xu, Kedai
1995
Furstenberg-Khasminskii formulas for Lyapunov exponents via anticipative calculus. Zbl 0857.60052
Arnold, Ludwig; Imkeller, Peter
1995
Anticipative problems in the theory of random dynamical systems. Zbl 0821.60062
Arnold, Ludwig
1995
Generation of random dynamical systems. Zbl 0864.60044
Arnold, Ludwig
1995
Evolutionary formalism for products of positive random matrices. Zbl 0818.15015
Arnold, Ludwig; Gundlach, Volker Matthias; Demetrius, Lloyd
1994
Random dynamical systems. Zbl 0805.60048
Arnold, L.
1994
Generic properties of Lyapunov exponents. Zbl 0827.58030
Arnold, Ludwig; Nguyen Dinh Cong
1994
Invariant measures for random dynamical systems, and a necessary condition for stochastic bifurcation from a fixed point. Zbl 0807.58022
Arnold, Ludwig; Xu, Kedai
1994
Simultaneous normal form and center manifold reduction for random differential equations. Zbl 0938.60512
Arnold, Ludwig; Xu, Kedai
1993
Iterated function systems and multiplicative ergodic theory. Zbl 0760.60008
Arnold, Ludwig; Crauel, Hans
1992
Stochastic bifurcation: Instructive examples in dimension one. Zbl 0751.60057
Arnold, Ludwig; Boxler, Petra
1992
Normal forms for random diffeomorphisms. Zbl 0763.34026
Arnold, Ludwig; Xu, Kedai
1992
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
Arnold, Ludwig (ed.); Crauel, Hans (ed.); Eckmann, Jean-Pierre (ed.)
1991
Additive noise turns a hyperbolic fixed point into a stationary solution. Zbl 0741.34010
Arnold, Ludwig; Boxler, Petra
1991
Stabilization by noise revisited. Zbl 0765.93076
Arnold, L.
1990
Stochastic differential equations as dynamical systems. Zbl 0727.93070
Arnold, Ludwig
1990
Lyapunov exponents and rotation number of two-dimensional systems with telegraphic noise. Zbl 0684.60046
Arnold, Ludwig; Kloeden, Peter
1989
A multiplicative ergodic theorem for rotation numbers. Zbl 0684.34059
Arnold, Ludwig; San Martin, Luiz
1989
Eigenvalues, bifurcation, and center manifolds in the presence of noise. Zbl 0681.60055
Arnold, Ludwig; Boxler, Petra
1989
On unique ergodicity for degenerate diffusions. Zbl 0617.60076
Arnold, Ludwig; Kliemann, Wolfgang
1987
Large deviations of linear stochastic differential equations. Zbl 0632.60021
Arnold, Ludwig; Kliemann, Wolfgang
1987
Asymptotic analysis of the Lyapunov exponent and rotation number of the random oscillator and applications. Zbl 0603.60051
Arnold, Ludwig; Papanicolaou, George; Wihstutz, Volker
1986
Lyapunov exponents: A survey. Zbl 0599.60061
Arnold, Ludwig; Wihstutz, Volker
1986
Lyapunov exponents of linear stochastic systems. Zbl 0588.60047
Arnold, L.; Kliemann, W.; Oeljeklaus, Eberhard
1986
Almost sure and moment stability for linear Ito equations. Zbl 0588.60049
Arnold, L.; Oeljeklaus, Eberhard; Pardoux, E.
1986
Lyapunov exponents. Proceedings of a Workshop held in Bremen, Germany, November 12-15, 1984. Zbl 0577.00017
Arnold, Ludwig (ed.); Wihstutz, Volker (ed.)
1986
A control problem related to the Lyapunov spectrum of stochastic flows. Zbl 0641.93069
San Martin, Luiz; Arnold, Ludwig
1986
A formula connecting sample and moment stability of linear stochastic systems. Zbl 0561.93063
Arnold, Ludwig
1984
Stochastic systems: qualitative theory and Lyapunov exponents. Zbl 0568.93068
Arnold, L.
1984
Stabilization of linear systems by noise. Zbl 0514.93069
Arnold, Ludwig; Crauel, Hans; Wihstutz, Volker
1983
Qualitative theory of stochastic systems. Zbl 0536.60070
Arnold, Ludwig; Kliemann, Wolfgang
1983
Wide sense stationary solutions of linear systems with additive noise. Zbl 0517.93050
Arnold, Ludwig; Wihstutz, Volker
1983
Stationary solutions of linear systems with additive and multiplicative noise. Zbl 0479.60061
Arnold, Ludwig; Wihstutz, Volker
1982
Stochastic nonlinear systems in physics, chemistry, and biology. Proceedings of the Workshop, Bielefeld, Fed. Rep. of Germany, October 5- 11, 1980. Zbl 0453.00034
Arnold, L. (ed.); Lefever, R. (ed.)
1981
Linear stochastic evolution equation models for chemical reactions. Zbl 0461.60079
Arnold, Ludwig; Kotelenez, P.; Curtain, Ruth F.
1981
Qualitative theory of stochastic non-linear systems. Zbl 0457.60037
Arnold, Ludwig
1981
Deterministic limit of the stochastic model of chemical reactions with diffusion. Zbl 0429.60025
Arnold, L.; Theodosopulu, M.
1980
On the consistency of the mathematical models of chemical reactions. Zbl 0498.93052
Arnold, L.
1980
The influence of external real and white noise on the Lotka-Volterra model. Zbl 0433.92019
Arnold, L.; Horsthemke, W.; Stuckl, J. W.
1979
A new example of an unstable system being stabilized by random parameter noise. Zbl 0424.93059
Arnold, L.
1979
Deterministic version of Wigner’s semicircle law for the distribution of matrix eigenvalues. Zbl 0332.15009
Arnold, Ludwig
1976
Stochastic differential equations: Theory and applications. Translation. Zbl 0278.60039
Arnold, Ludwig
1974
Stochastische Differentialgleichungen. Theorie und Anwendung. Zbl 0266.60039
Arnold, Ludwig
1973
On Wigner’s semicircle law for the eigenvalues of random matrices. Zbl 0212.51006
Arnold, L.
1971
On Wigner’s semicircle law for the eigenvalues of random matrices. Zbl 0206.48202
Arnold, L.
1971
The log law for multidimensional stochastic integrals and diffusion processes. Zbl 0219.60047
Arnold, L.
1971
Complex-valued stable measures and their domains of attraction. Zbl 0174.19102
Arnold, Ludwig; Michaliček, Johannes
1969
On Fredholm integral equations with random degenerate kernels. Zbl 0224.60029
Bharucha-Reid, A. T.; Arnold, L.
1969
On the norm of stable measures. Zbl 0162.45301
Arnold, Ludwig; Michaliček, Johannes
1968
On the asymptotic distribution of the eigenvalues of random matrices. Zbl 0246.60029
Arnold, Ludwig
1967
Über die Konvergenz einer zufälligen Potenzreihe. Zbl 0146.38803
Arnold, Ludwig
1966
Über die Nullstellenverteilung zufälliger Polynome. Zbl 0139.35801
Arnold, Ludwig
1966
Wachstumseigenschaften zufälliger ganzer Funktionen. Zbl 0203.17103
Arnold, Ludwig
1966
Konvergenzprobleme bei zufälligen Potenzreihen mit Lücken. Zbl 0146.38901
Arnold, Ludwig
1966
Digitale Simulation des Verkehrsablaufes auf einer Landstraße. Zbl 0122.13103
Arnold, L.; Resz, H.
1964
Numerische Experimente zur mehrdimensionalen Quadratur. Zbl 0128.36902
Roos, P.; Arnold, L.
1963
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#### Cited by 2,313 Authors

 34 Caraballo Garrido, Tomás 33 Duan, Jinqiao 30 Kloeden, Peter Eris 30 Wang, Bixiang 27 Zhou, Shengfan 25 Schmalfuß, Björn 24 Lu, Kening 23 Mao, Xuerong 22 Arnold, Ludwig 20 Li, Yangrong 19 Langa, Jose’ Antonio 19 Scheutzow, Michael K. R. 18 Jiang, Daqing 14 Gu, Anhui 14 Schurz, Henri 13 Bashkirtseva, Irina Adol’fovna 13 Cortés López, Juan Carlos 13 Han, Xiaoying 13 Jimenez, Juan Carlos 13 Obaya, Rafael 13 Rasmussen, Martin 13 Ryashko, Lev Borisovich 12 Garrido-Atienza, María José 12 Jódar Sanchez, Lucas Antonio 12 Kliemann, Wolfgang H. 11 Huang, Zaitang 11 Namachchivaya, N. Sri 11 Singer, Hermann 11 Valero, José 11 Wang, Zhaojuan 11 Wu, Fuke 11 Zhao, Wenqiang 10 Buckwar, Evelyn 10 Chueshov, Igor’ Dmitrievich 10 Colonius, Fritz 10 Crauel, Hans 10 Flandoli, Franco 10 Gess, Benjamin 10 Xu, Wei 9 Cao, Junfei 9 Evstigneev, Igor V. 9 Ji, Chunyan 9 Liu, Xianbin 9 Mierczyński, Janusz 9 Mohammed, Salah-Eldin A. 9 Nguyen Dinh Cong 9 Schenk-Hoppé, Klaus Reiner 9 Shen, Wenxian 9 Tocino, Alicia 9 Villafuerte, Laura 9 Wang, Ke 9 Yang, Meihua 9 Yang, Qigui 8 Baxendale, Peter H. 8 Braumann, Carlos A. 8 Florchinger, Patrick 8 Li, Dingshi 8 Liu, Zhenxin 8 Wang, Wei 8 Wang, Xiaohu 8 Wihstutz, Volker 7 Bates, Peter W. 7 Biscay, Rolando J. 7 Brzeźniak, Zdzisław 7 Cui, Hongyong 7 Guo, Boling 7 Imkeller, Peter 7 Li, Weigu 7 Liu, Qun 7 Lv, Yan 7 Novo, Sylvia 7 Robinson, James Cooper 7 San Martin, Luiz Antonio Barrera 7 Sanz, Ana M. 7 Shi, Ningzhong 7 Spigler, Renato 7 Zhao, Huaizhong 6 Appleby, John A. D. 6 Bochi, Jairo 6 Carbonell, Felix 6 Chekroun, Mickaël D. 6 Doan, Thai Son 6 Ghil, Michael 6 Komori, Yoshio 6 Kotelenez, Peter M. 6 Liu, Xianming 6 Nguyen Huu Du 6 Rodkina, Alexandra 6 Siegmund, Stefan 6 You, Yuncheng 5 Albeverio, Sergio A. 5 Bessaih, Hakima 5 Demetrius, Lloyd A. 5 Deng, Feiqi 5 Gaeta, Giuseppe 5 Guzik, Grzegorz 5 Hairer, Martin 5 Hmissi, Mohamed 5 Homburg, Ale Jan 5 Jentzen, Arnulf ...and 2,213 more Authors
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#### Cited in 372 Serials

 81 Journal of Differential Equations 70 Stochastic Analysis and Applications 58 Journal of Mathematical Analysis and Applications 55 Stochastics and Dynamics 52 Discrete and Continuous Dynamical Systems. Series B 50 Stochastic Processes and their Applications 40 Physica D 39 Journal of Statistical Physics 37 Discrete and Continuous Dynamical Systems 36 Journal of Computational and Applied Mathematics 33 Journal of Dynamics and Differential Equations 28 Mathematical Biosciences 27 Applied Mathematics and Computation 27 Systems & Control Letters 25 Proceedings of the American Mathematical Society 24 Nonlinear Dynamics 23 Chaos, Solitons and Fractals 23 The Annals of Probability 22 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 20 Automatica 20 Probability Theory and Related Fields 17 International Journal of Control 17 Journal of Mathematical Physics 17 Transactions of the American Mathematical Society 17 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 17 Chaos 15 Computers & Mathematics with Applications 15 Applied Mathematical Modelling 15 Abstract and Applied Analysis 14 Physica A 14 BIT 14 Journal of Functional Analysis 14 Mathematics and Computers in Simulation 14 Mathematical and Computer Modelling 13 Journal of Computational Physics 13 Physics Letters. A 13 Insurance Mathematics & Economics 13 Journal of Economic Dynamics & Control 13 Journal of Difference Equations and Applications 13 Communications on Pure and Applied Analysis 12 Stochastics 12 Bulletin of Mathematical Biology 12 Ergodic Theory and Dynamical Systems 11 The Annals of Applied Probability 11 Linear Algebra and its Applications 11 Dynamical Systems 10 Communications in Mathematical Physics 10 International Journal of Systems Science 10 Journal of the Franklin Institute 10 Journal of Mathematical Biology 10 Theoretical Population Biology 10 Applied Mathematics Letters 10 Stochastic Hydrology and Hydraulics 10 Stochastics and Stochastics Reports 10 Nonlinear Analysis. Real World Applications 9 Mathematische Zeitschrift 8 Nonlinearity 8 Physics Reports 8 SIAM Journal on Control and Optimization 8 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 8 Journal of Theoretical Probability 8 Journal of Nonlinear Science 8 Mathematical Problems in Engineering 8 SIAM Journal on Applied Dynamical Systems 8 Advances in Difference Equations 7 Applied Mathematics and Mechanics. (English Edition) 7 Acta Applicandae Mathematicae 7 European Journal of Operational Research 7 Acta Mathematica Sinica. English Series 7 Communications in Nonlinear Science and Numerical Simulation 6 Journal of Approximation Theory 6 Journal of Mathematical Economics 6 The Journal of Mathematical Sociology 6 Statistics & Probability Letters 6 Applied Numerical Mathematics 6 Annals of Physics 6 SIAM Journal on Mathematical Analysis 6 International Journal of Robust and Nonlinear Control 6 Journal of Nonlinear Mathematical Physics 5 International Journal of Engineering Science 5 Archiv der Mathematik 5 Journal of Optimization Theory and Applications 5 Statistica Neerlandica 5 Dynamics and Stability of Systems 5 MCSS. Mathematics of Control, Signals, and Systems 5 Communications in Statistics. Theory and Methods 5 Journal of Mathematical Sciences (New York) 5 Random Operators and Stochastic Equations 5 European Journal of Control 5 Differential Equations and Dynamical Systems 5 Frontiers of Mathematics in China 5 Discrete and Continuous Dynamical Systems. Series S 5 Journal of Applied Analysis and Computation 4 Computer Methods in Applied Mechanics and Engineering 4 Ingenieur-Archiv 4 Israel Journal of Mathematics 4 Annals of the Institute of Statistical Mathematics 4 Applied Mathematics and Optimization 4 Journal of Mathematical Psychology 4 Journal of Multivariate Analysis ...and 272 more Serials
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#### Cited in 51 Fields

 1,066 Probability theory and stochastic processes (60-XX) 653 Dynamical systems and ergodic theory (37-XX) 415 Ordinary differential equations (34-XX) 335 Systems theory; control (93-XX) 307 Partial differential equations (35-XX) 216 Biology and other natural sciences (92-XX) 193 Numerical analysis (65-XX) 106 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 89 Statistics (62-XX) 82 Fluid mechanics (76-XX) 63 Statistical mechanics, structure of matter (82-XX) 49 Linear and multilinear algebra; matrix theory (15-XX) 42 Operator theory (47-XX) 40 Mechanics of particles and systems (70-XX) 34 Mechanics of deformable solids (74-XX) 32 Quantum theory (81-XX) 32 Geophysics (86-XX) 29 Difference and functional equations (39-XX) 28 Calculus of variations and optimal control; optimization (49-XX) 25 Operations research, mathematical programming (90-XX) 23 Global analysis, analysis on manifolds (58-XX) 22 Measure and integration (28-XX) 20 Functional analysis (46-XX) 16 Combinatorics (05-XX) 16 Information and communication theory, circuits (94-XX) 15 Computer science (68-XX) 14 Functions of a complex variable (30-XX) 11 Integral equations (45-XX) 10 Real functions (26-XX) 10 Classical thermodynamics, heat transfer (80-XX) 6 Approximations and expansions (41-XX) 6 General topology (54-XX) 5 Topological groups, Lie groups (22-XX) 5 Abstract harmonic analysis (43-XX) 5 Manifolds and cell complexes (57-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Differential geometry (53-XX) 3 History and biography (01-XX) 3 Number theory (11-XX) 3 Special functions (33-XX) 3 Relativity and gravitational theory (83-XX) 2 General and overarching topics; collections (00-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Integral transforms, operational calculus (44-XX) 2 Astronomy and astrophysics (85-XX) 1 Category theory; homological algebra (18-XX) 1 Group theory and generalizations (20-XX) 1 Sequences, series, summability (40-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) 1 Optics, electromagnetic theory (78-XX)