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Author ID: arnold.ludwig Recent zbMATH articles by "Arnold, Ludwig"
Published as: Arnold, Ludwig; Arnold, L.
External Links: MGP
Documents Indexed: 97 Publications since 1963, including 3 Books
4 Contributions as Editor
Reviewing Activity: 32 Reviews
Biographic References: 2 Publications
Co-Authors: 38 Co-Authors with 65 Joint Publications
1,050 Co-Co-Authors
all top 5

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 Mathematics and its Applications (Dordrecht)
1 Springer Series in Synergetics
1 Advances in Operator Theory
1 Springer Monographs in Mathematics

Publications by Year

Citations contained in zbMATH Open

92 Publications have been cited 3,479 times in 2,957 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
774
1974
Stabilization of linear systems by noise. Zbl 0514.93069
Arnold, Ludwig; Crauel, Hans; Wihstutz, Volker
105
1983
The influence of external real and white noise on the Lotka-Volterra model. Zbl 0433.92019
Arnold, L.; Horsthemke, W.; Stuckl, J. W.
62
1979
A formula connecting sample and moment stability of linear stochastic systems. Zbl 0561.93063
Arnold, Ludwig
54
1984
Toward an understanding of stochastic Hopf bifurcation: a case study. Zbl 1298.37038
Arnold, Ludwig; Namachchivaya, N. Sri; Schenk-Hoppé, Klaus R.
50
1996
Evolutionary formalism for products of positive random matrices. Zbl 0818.15015
Arnold, Ludwig; Gundlach, Volker Matthias; Demetrius, Lloyd
49
1994
On the asymptotic distribution of the eigenvalues of random matrices. Zbl 0246.60029
Arnold, Ludwig
47
1967
Asymptotic analysis of the Lyapunov exponent and rotation number of the random oscillator and applications. Zbl 0603.60051
Arnold, Ludwig; Papanicolaou, George; Wihstutz, Volker
46
1986
Stationary and almost periodic solutions of almost periodic affine stochastic differential equations. Zbl 1043.60513
Arnold, Ludwig; Tudor, Constantin
40
1998
Order-preserving random dynamical systems: Equilibria, attractors, applications. Zbl 0938.37031
Arnold, Ludwig; Chueshov, Igor
40
1998
Perfect cocycles through stochastic differential equations. Zbl 0821.60061
Arnold, Ludwig; Scheutzow, Michael
39
1995
Lyapunov exponents of linear stochastic systems. Zbl 0588.60047
Arnold, L.; Kliemann, W.; Oeljeklaus, Eberhard
38
1986
Almost sure and moment stability for linear Ito equations. Zbl 0588.60049
Arnold, L.; Oeljeklaus, Eberhard; Pardoux, E.
35
1986
Lyapunov exponents: A survey. Zbl 0599.60061
Arnold, Ludwig; Wihstutz, Volker
35
1986
Random dynamical systems. Zbl 0834.58026
Arnold, Ludwig
34
1995
On unique ergodicity for degenerate diffusions. Zbl 0617.60076
Arnold, Ludwig; Kliemann, Wolfgang
32
1987
Stochastische Differentialgleichungen. Theorie und Anwendung. Zbl 0266.60039
Arnold, Ludwig
31
1973
Deterministic limit of the stochastic model of chemical reactions with diffusion. Zbl 0429.60025
Arnold, L.; Theodosopulu, M.
30
1980
Random dynamical systems. Zbl 0736.58029
Arnold, Ludwig; Crauel, Hans
29
1991
Stabilization by noise revisited. Zbl 0765.93076
Arnold, L.
27
1990
Lyapunov’s second method for random dynamical systems. Zbl 1040.37035
Arnold, Ludwig; Schmalfuss, Björn
26
2001
Normal forms for stochastic differential equations. Zbl 0906.60048
Arnold, Ludwig; Imkeller, Peter
26
1998
Hasselmann’s program revisited: The analysis of stochasticity in deterministic climate models. Zbl 1015.34037
Arnold, Ludwig
24
2001
Qualitative theory of stochastic systems. Zbl 0536.60070
Arnold, Ludwig; Kliemann, Wolfgang
21
1983
Small noise expansion of moment Lyapunov exponents for two-dimensional systems. Zbl 0890.60055
Arnold, L.; Doyle, M. M.; Sri Namachchivaya, N.
20
1997
On Wigner’s semicircle law for the eigenvalues of random matrices. Zbl 0212.51006
Arnold, L.
19
1971
On Wigner’s semicircle law for the eigenvalues of random matrices. Zbl 0206.48202
Arnold, L.
17
1971
Iterated function systems and multiplicative ergodic theory. Zbl 0760.60008
Arnold, Ludwig; Crauel, Hans
16
1992
Stochastic nonlinear systems in physics, chemistry, and biology. Proceedings of the Workshop, Bielefeld, Fed. Rep. of Germany, October 5- 11, 1980. Zbl 0453.00034
15
1981
Über die Nullstellenverteilung zufälliger Polynome. Zbl 0139.35801
Arnold, Ludwig
15
1966
The stochastic Brusselator: Parametric noise destroys Hopf bifurcation. Zbl 0939.60057
Arnold, Ludwig; Bleckert, Gabriele; Schenk-Hoppé, Klaus Reiner
14
1999
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
13
2003
Über die Konvergenz einer zufälligen Potenzreihe. Zbl 0146.38803
Arnold, Ludwig
13
1966
Jordan normal form for linear cocycles. Zbl 0971.37002
Arnold, Ludwig; Nguyen Dinh Cong; Oseledets, Valery
12
1999
Stratonovich calculus with spatial parameters and anticipative problems in multiplicative ergodic theory. Zbl 0847.60037
Arnold, Ludwig; Imkeller, Peter
11
1996
Stability and capsizing of ships in random sea – a survey. Zbl 1090.70014
Arnold, Ludwig; Chueshov, Igor; Ochs, Gunter
11
2004
Random dynamical systems. (Zufällige dynamische Systeme.) Zbl 0805.60048
Arnold, L.
11
1994
Large deviations of linear stochastic differential equations. Zbl 0632.60021
Arnold, Ludwig; Kliemann, Wolfgang
11
1987
Linear cocycles with simple Lyapunov spectrum are dense in \(L^\infty\). Zbl 0952.37002
Arnold, Ludwig; Nguyen Dinh Cong
11
1999
Lyapunov exponents. Proceedings of a Workshop held in Bremen, Germany, November 12-15, 1984. Zbl 0577.00017
10
1986
The asymptotic stability of a noisy non-linear oscillator. Zbl 1236.70044
Arnold, L.; Imkeller, P.; Namachchivaya, N. Sri
10
2004
Stochastic bifurcation: Instructive examples in dimension one. Zbl 0751.60057
Arnold, Ludwig; Boxler, Petra
9
1992
A multiplicative ergodic theorem for rotation numbers. Zbl 0684.34059
Arnold, Ludwig; San Martin, Luiz
9
1989
Lyapunov exponents and rotation number of two-dimensional systems with telegraphic noise. Zbl 0684.60046
Arnold, Ludwig; Kloeden, Peter
9
1989
On the simplicity of the Lyapunov spectrum of products of random matrices. Zbl 0891.58022
Arnold, Ludwig; Cong, Nguyen Dinh
9
1997
On the consistency of the mathematical models of chemical reactions. Zbl 0498.93052
Arnold, L.
9
1980
Cooperative random and stochastic differential equations. Zbl 1017.37026
Arnold, Ludwig; Chueshov, Igor
8
2001
Lyapunov exponents. Proceedings of a conference, held in Oberwolfach, Germany, May 28-June 2, 1990. Zbl 0733.00015
8
1991
Convex-valued random dynamical systems: A variational principle for equilibrium states. Zbl 0933.93063
Arnold, L.; Evstigneev, I. V.; Gundlach, V. M.
7
1999
Fixed points and attractors for random dynamical systems. Zbl 0925.58050
Arnold, L.; Schmalfuss, B.
7
1996
Stability index for nonlinear stochastic differential equations. Zbl 0827.93065
Arnold, Ludwig; Khasminskii, Rafail Z.
6
1995
Normal forms for random diffeomorphisms. Zbl 0763.34026
Arnold, Ludwig; Xu, Kedai
6
1992
Stationary solutions of linear systems with additive and multiplicative noise. Zbl 0479.60061
Arnold, Ludwig; Wihstutz, Volker
6
1982
Deterministic version of Wigner’s semicircle law for the distribution of matrix eigenvalues. Zbl 0332.15009
Arnold, Ludwig
6
1976
Stochastic systems: qualitative theory and Lyapunov exponents. Zbl 0568.93068
Arnold, L.
6
1984
Normal forms for random differential equations. Zbl 0820.34037
Arnold, Ludwig; Xu, Kedai
5
1995
Recent progress in stochastic bifurcation theory. Zbl 1226.70009
Arnold, Ludwig
5
2001
A limit set trichotomy for order-preserving random systems. Zbl 0997.34044
Arnold, Ludwig; Chueshov, Igor
5
2001
Lyapunov exponents of nonlinear stochastic systems. Zbl 0661.93075
Arnold, L.
5
1989
A control problem related to the Lyapunov spectrum of stochastic flows. Zbl 0641.93069
San Martin, Luiz; Arnold, Ludwig
5
1986
The log law for multidimensional stochastic integrals and diffusion processes. Zbl 0219.60047
Arnold, L.
5
1971
Additive noise turns a hyperbolic fixed point into a stationary solution. Zbl 0741.34010
Arnold, Ludwig; Boxler, Petra
4
1991
Generic properties of Lyapunov exponents. Zbl 0827.58030
Arnold, Ludwig; Nguyen Dinh Cong
4
1994
Discretization of a random dynamical system near a hyperbolic point. Zbl 0857.34058
Arnold, Ludwig; Kloeden, Peter
4
1996
A new example of an unstable system being stabilized by random parameter noise. Zbl 0424.93059
Arnold, L.
4
1979
Trends and open problems in the theory of random dynamical systems. Zbl 1044.37516
Arnold, Ludwig
4
1998
Random dynamical systems methods in ship stability: a case study. Zbl 1092.34028
Arnold, Ludwig; Chueshov, Igor; Ochs, Gunter
4
2005
Wachstumseigenschaften zufälliger ganzer Funktionen. Zbl 0203.17103
Arnold, Ludwig
4
1966
Anticipative problems in the theory of random dynamical systems. Zbl 0821.60062
Arnold, Ludwig
3
1995
Stochastic differential equations as dynamical systems. Zbl 0727.93070
Arnold, Ludwig
3
1990
Simultaneous normal form and center manifold reduction for random differential equations. Zbl 0938.60512
Arnold, Ludwig; Xu, Kedai
3
1993
Linear and nonlinear diffusion approximation of the slow motion in systems with two time scales. Zbl 1079.34046
Arnold, Ludwig
3
2003
Linear stochastic evolution equation models for chemical reactions. Zbl 0461.60079
Arnold, Ludwig; Kotelenez, P.; Curtain, Ruth F.
3
1981
Eigenvalues, bifurcation, and center manifolds in the presence of noise. Zbl 0681.60055
Arnold, Ludwig; Boxler, Petra
3
1989
Large noise asymptotics of invariant measures, with applications to Lyapunov exponents. Zbl 0869.93051
Arnold, Ludwig; Eizenberg, Alex; Wihstutz, Volker
3
1996
Numerische Experimente zur mehrdimensionalen Quadratur. Zbl 0128.36902
Roos, P.; Arnold, L.
3
1963
Complex-valued stable measures and their domains of attraction. Zbl 0174.19102
Arnold, Ludwig; Michaliček, Johannes
3
1969
Furstenberg-Khasminskii formulas for Lyapunov exponents via anticipative calculus. Zbl 0857.60052
Arnold, Ludwig; Imkeller, Peter
3
1995
Behavior of Kreiss bounded \(C_0\)-semigroups on a Hilbert space. Zbl 1509.47063
Arnold, L.
3
2022
Rotation numbers for linear stochastic differential equations. Zbl 0944.60065
Arnold, Ludwig; Imkeller, Peter
3
1999
On the integrability condition in the multiplicative ergodic theorem for stochastic differential equations. Zbl 1043.60512
Arnold, Ludwig; Imkeller, Peter
2
1998
The possible asymptotic distributions of eigenvalues of random symmetric matrices. Zbl 0286.15003
Arnold, Ludwig
2
1973
Konvergenzprobleme bei zufälligen Potenzreihen mit Lücken. Zbl 0146.38901
Arnold, Ludwig
2
1966
Wide sense stationary solutions of linear systems with additive noise. Zbl 0517.93050
Arnold, Ludwig; Wihstutz, Volker
2
1983
The essential range of a nonabelian cocycle is not a cohomology invariant. Zbl 0989.37002
Arnold, L.; Nguyen Dinh Cong; Oseledets, V. I.
1
2000
Invariant measures for random dynamical systems, and a necessary condition for stochastic bifurcation from a fixed point. Zbl 0807.58022
Arnold, Ludwig; Xu, Kedai
1
1994
Qualitative theory of stochastic non-linear systems. Zbl 0457.60037
Arnold, Ludwig
1
1981
The unfolding of dynamics in stochastic analysis. Zbl 0874.60048
Arnold, Ludwig
1
1997
Digitale Simulation des Verkehrsablaufes auf einer Landstraße. Zbl 0122.13103
Arnold, L.; Resz, H.
1
1964
On the norm of stable measures. Zbl 0162.45301
Arnold, Ludwig; Michaliček, Johannes
1
1968
On Fredholm integral equations with random degenerate kernels. Zbl 0224.60029
Bharucha-Reid, A. T.; Arnold, L.
1
1969
Behavior of Kreiss bounded \(C_0\)-semigroups on a Hilbert space. Zbl 1509.47063
Arnold, L.
3
2022
Random dynamical systems methods in ship stability: a case study. Zbl 1092.34028
Arnold, Ludwig; Chueshov, Igor; Ochs, Gunter
4
2005
Stability and capsizing of ships in random sea – a survey. Zbl 1090.70014
Arnold, Ludwig; Chueshov, Igor; Ochs, Gunter
11
2004
The asymptotic stability of a noisy non-linear oscillator. Zbl 1236.70044
Arnold, L.; Imkeller, P.; Namachchivaya, N. Sri
10
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
13
2003
Linear and nonlinear diffusion approximation of the slow motion in systems with two time scales. Zbl 1079.34046
Arnold, Ludwig
3
2003
Lyapunov’s second method for random dynamical systems. Zbl 1040.37035
Arnold, Ludwig; Schmalfuss, Björn
26
2001
Hasselmann’s program revisited: The analysis of stochasticity in deterministic climate models. Zbl 1015.34037
Arnold, Ludwig
24
2001
Cooperative random and stochastic differential equations. Zbl 1017.37026
Arnold, Ludwig; Chueshov, Igor
8
2001
Recent progress in stochastic bifurcation theory. Zbl 1226.70009
Arnold, Ludwig
5
2001
A limit set trichotomy for order-preserving random systems. Zbl 0997.34044
Arnold, Ludwig; Chueshov, Igor
5
2001
The essential range of a nonabelian cocycle is not a cohomology invariant. Zbl 0989.37002
Arnold, L.; Nguyen Dinh Cong; Oseledets, V. I.
1
2000
The stochastic Brusselator: Parametric noise destroys Hopf bifurcation. Zbl 0939.60057
Arnold, Ludwig; Bleckert, Gabriele; Schenk-Hoppé, Klaus Reiner
14
1999
Jordan normal form for linear cocycles. Zbl 0971.37002
Arnold, Ludwig; Nguyen Dinh Cong; Oseledets, Valery
12
1999
Linear cocycles with simple Lyapunov spectrum are dense in \(L^\infty\). Zbl 0952.37002
Arnold, Ludwig; Nguyen Dinh Cong
11
1999
Convex-valued random dynamical systems: A variational principle for equilibrium states. Zbl 0933.93063
Arnold, L.; Evstigneev, I. V.; Gundlach, V. M.
7
1999
Rotation numbers for linear stochastic differential equations. Zbl 0944.60065
Arnold, Ludwig; Imkeller, Peter
3
1999
Random dynamical systems. Zbl 0906.34001
Arnold, Ludwig
1998
Stationary and almost periodic solutions of almost periodic affine stochastic differential equations. Zbl 1043.60513
Arnold, Ludwig; Tudor, Constantin
40
1998
Order-preserving random dynamical systems: Equilibria, attractors, applications. Zbl 0938.37031
Arnold, Ludwig; Chueshov, Igor
40
1998
Normal forms for stochastic differential equations. Zbl 0906.60048
Arnold, Ludwig; Imkeller, Peter
26
1998
Trends and open problems in the theory of random dynamical systems. Zbl 1044.37516
Arnold, Ludwig
4
1998
On the integrability condition in the multiplicative ergodic theorem for stochastic differential equations. Zbl 1043.60512
Arnold, Ludwig; Imkeller, Peter
2
1998
Small noise expansion of moment Lyapunov exponents for two-dimensional systems. Zbl 0890.60055
Arnold, L.; Doyle, M. M.; Sri Namachchivaya, N.
20
1997
On the simplicity of the Lyapunov spectrum of products of random matrices. Zbl 0891.58022
Arnold, Ludwig; Cong, Nguyen Dinh
9
1997
The unfolding of dynamics in stochastic analysis. Zbl 0874.60048
Arnold, Ludwig
1
1997
Toward an understanding of stochastic Hopf bifurcation: a case study. Zbl 1298.37038
Arnold, Ludwig; Namachchivaya, N. Sri; Schenk-Hoppé, Klaus R.
50
1996
Stratonovich calculus with spatial parameters and anticipative problems in multiplicative ergodic theory. Zbl 0847.60037
Arnold, Ludwig; Imkeller, Peter
11
1996
Fixed points and attractors for random dynamical systems. Zbl 0925.58050
Arnold, L.; Schmalfuss, B.
7
1996
Discretization of a random dynamical system near a hyperbolic point. Zbl 0857.34058
Arnold, Ludwig; Kloeden, Peter
4
1996
Large noise asymptotics of invariant measures, with applications to Lyapunov exponents. Zbl 0869.93051
Arnold, Ludwig; Eizenberg, Alex; Wihstutz, Volker
3
1996
Perfect cocycles through stochastic differential equations. Zbl 0821.60061
Arnold, Ludwig; Scheutzow, Michael
39
1995
Random dynamical systems. Zbl 0834.58026
Arnold, Ludwig
34
1995
Stability index for nonlinear stochastic differential equations. Zbl 0827.93065
Arnold, Ludwig; Khasminskii, Rafail Z.
6
1995
Normal forms for random differential equations. Zbl 0820.34037
Arnold, Ludwig; Xu, Kedai
5
1995
Anticipative problems in the theory of random dynamical systems. Zbl 0821.60062
Arnold, Ludwig
3
1995
Furstenberg-Khasminskii formulas for Lyapunov exponents via anticipative calculus. Zbl 0857.60052
Arnold, Ludwig; Imkeller, Peter
3
1995
Evolutionary formalism for products of positive random matrices. Zbl 0818.15015
Arnold, Ludwig; Gundlach, Volker Matthias; Demetrius, Lloyd
49
1994
Random dynamical systems. (Zufällige dynamische Systeme.) Zbl 0805.60048
Arnold, L.
11
1994
Generic properties of Lyapunov exponents. Zbl 0827.58030
Arnold, Ludwig; Nguyen Dinh Cong
4
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
1
1994
Simultaneous normal form and center manifold reduction for random differential equations. Zbl 0938.60512
Arnold, Ludwig; Xu, Kedai
3
1993
Iterated function systems and multiplicative ergodic theory. Zbl 0760.60008
Arnold, Ludwig; Crauel, Hans
16
1992
Stochastic bifurcation: Instructive examples in dimension one. Zbl 0751.60057
Arnold, Ludwig; Boxler, Petra
9
1992
Normal forms for random diffeomorphisms. Zbl 0763.34026
Arnold, Ludwig; Xu, Kedai
6
1992
Random dynamical systems. Zbl 0736.58029
Arnold, Ludwig; Crauel, Hans
29
1991
Lyapunov exponents. Proceedings of a conference, held in Oberwolfach, Germany, May 28-June 2, 1990. Zbl 0733.00015
8
1991
Additive noise turns a hyperbolic fixed point into a stationary solution. Zbl 0741.34010
Arnold, Ludwig; Boxler, Petra
4
1991
Stabilization by noise revisited. Zbl 0765.93076
Arnold, L.
27
1990
Stochastic differential equations as dynamical systems. Zbl 0727.93070
Arnold, Ludwig
3
1990
A multiplicative ergodic theorem for rotation numbers. Zbl 0684.34059
Arnold, Ludwig; San Martin, Luiz
9
1989
Lyapunov exponents and rotation number of two-dimensional systems with telegraphic noise. Zbl 0684.60046
Arnold, Ludwig; Kloeden, Peter
9
1989
Lyapunov exponents of nonlinear stochastic systems. Zbl 0661.93075
Arnold, L.
5
1989
Eigenvalues, bifurcation, and center manifolds in the presence of noise. Zbl 0681.60055
Arnold, Ludwig; Boxler, Petra
3
1989
On unique ergodicity for degenerate diffusions. Zbl 0617.60076
Arnold, Ludwig; Kliemann, Wolfgang
32
1987
Large deviations of linear stochastic differential equations. Zbl 0632.60021
Arnold, Ludwig; Kliemann, Wolfgang
11
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
46
1986
Lyapunov exponents of linear stochastic systems. Zbl 0588.60047
Arnold, L.; Kliemann, W.; Oeljeklaus, Eberhard
38
1986
Almost sure and moment stability for linear Ito equations. Zbl 0588.60049
Arnold, L.; Oeljeklaus, Eberhard; Pardoux, E.
35
1986
Lyapunov exponents: A survey. Zbl 0599.60061
Arnold, Ludwig; Wihstutz, Volker
35
1986
Lyapunov exponents. Proceedings of a Workshop held in Bremen, Germany, November 12-15, 1984. Zbl 0577.00017
10
1986
A control problem related to the Lyapunov spectrum of stochastic flows. Zbl 0641.93069
San Martin, Luiz; Arnold, Ludwig
5
1986
A formula connecting sample and moment stability of linear stochastic systems. Zbl 0561.93063
Arnold, Ludwig
54
1984
Stochastic systems: qualitative theory and Lyapunov exponents. Zbl 0568.93068
Arnold, L.
6
1984
Stabilization of linear systems by noise. Zbl 0514.93069
Arnold, Ludwig; Crauel, Hans; Wihstutz, Volker
105
1983
Qualitative theory of stochastic systems. Zbl 0536.60070
Arnold, Ludwig; Kliemann, Wolfgang
21
1983
Wide sense stationary solutions of linear systems with additive noise. Zbl 0517.93050
Arnold, Ludwig; Wihstutz, Volker
2
1983
Stationary solutions of linear systems with additive and multiplicative noise. Zbl 0479.60061
Arnold, Ludwig; Wihstutz, Volker
6
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
15
1981
Linear stochastic evolution equation models for chemical reactions. Zbl 0461.60079
Arnold, Ludwig; Kotelenez, P.; Curtain, Ruth F.
3
1981
Qualitative theory of stochastic non-linear systems. Zbl 0457.60037
Arnold, Ludwig
1
1981
Deterministic limit of the stochastic model of chemical reactions with diffusion. Zbl 0429.60025
Arnold, L.; Theodosopulu, M.
30
1980
On the consistency of the mathematical models of chemical reactions. Zbl 0498.93052
Arnold, L.
9
1980
The influence of external real and white noise on the Lotka-Volterra model. Zbl 0433.92019
Arnold, L.; Horsthemke, W.; Stuckl, J. W.
62
1979
A new example of an unstable system being stabilized by random parameter noise. Zbl 0424.93059
Arnold, L.
4
1979
Deterministic version of Wigner’s semicircle law for the distribution of matrix eigenvalues. Zbl 0332.15009
Arnold, Ludwig
6
1976
Stochastic differential equations: Theory and applications. Translation. Zbl 0278.60039
Arnold, Ludwig
774
1974
Stochastische Differentialgleichungen. Theorie und Anwendung. Zbl 0266.60039
Arnold, Ludwig
31
1973
The possible asymptotic distributions of eigenvalues of random symmetric matrices. Zbl 0286.15003
Arnold, Ludwig
2
1973
On Wigner’s semicircle law for the eigenvalues of random matrices. Zbl 0212.51006
Arnold, L.
19
1971
On Wigner’s semicircle law for the eigenvalues of random matrices. Zbl 0206.48202
Arnold, L.
17
1971
The log law for multidimensional stochastic integrals and diffusion processes. Zbl 0219.60047
Arnold, L.
5
1971
Complex-valued stable measures and their domains of attraction. Zbl 0174.19102
Arnold, Ludwig; Michaliček, Johannes
3
1969
On Fredholm integral equations with random degenerate kernels. Zbl 0224.60029
Bharucha-Reid, A. T.; Arnold, L.
1
1969
On the norm of stable measures. Zbl 0162.45301
Arnold, Ludwig; Michaliček, Johannes
1
1968
On the asymptotic distribution of the eigenvalues of random matrices. Zbl 0246.60029
Arnold, Ludwig
47
1967
Über die Nullstellenverteilung zufälliger Polynome. Zbl 0139.35801
Arnold, Ludwig
15
1966
Über die Konvergenz einer zufälligen Potenzreihe. Zbl 0146.38803
Arnold, Ludwig
13
1966
Wachstumseigenschaften zufälliger ganzer Funktionen. Zbl 0203.17103
Arnold, Ludwig
4
1966
Konvergenzprobleme bei zufälligen Potenzreihen mit Lücken. Zbl 0146.38901
Arnold, Ludwig
2
1966
Digitale Simulation des Verkehrsablaufes auf einer Landstraße. Zbl 0122.13103
Arnold, L.; Resz, H.
1
1964
Numerische Experimente zur mehrdimensionalen Quadratur. Zbl 0128.36902
Roos, P.; Arnold, L.
3
1963
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Cited by 3,296 Authors

56 Caraballo Garrido, Tomás
47 Duan, Jinqiao
44 Wang, Bixiang
43 Li, Yangrong
42 Bashkirtseva, Irina Adol’fovna
42 Ryashko, Lev Borisovich
40 Kloeden, Peter Eris
40 Lu, Kening
35 Schmalfuß, Björn
35 Zhou, Shengfan
30 Mao, Xuerong
26 Scheutzow, Michael K. R.
26 Shu, Ji
24 Gu, Anhui
23 Arnold, Ludwig
23 Jiang, Daqing
23 Langa, Jose’ Antonio
22 Zhao, Wenqiang
21 Dragičević, Davor
21 Han, Xiaoying
20 Garrido-Atienza, María José
19 Schurz, Henri
18 Wang, Renhai
17 Li, Dingshi
17 Obaya, Rafael
16 Cortés López, Juan Carlos
16 Xu, Wei
16 Yang, Qigui
15 Gao, Hongjun
15 Li, Fuzhi
15 Wang, Xiaohu
14 Huang, Zaitang
14 Jódar Sanchez, Lucas Antonio
14 Rasmussen, Martin
14 Wang, Zhaojuan
14 Zeng, Caibin
14 Zhao, Huaizhong
13 Buckwar, Evelyn
13 Colonius, Fritz
13 Flandoli, Franco
13 Jimenez, Juan Carlos
13 Kliemann, Wolfgang H.
13 Liu, Zhenxin
13 Nguyen Dinh Cong
13 Shen, Jun
13 Shi, Lin
13 Valero, José
12 Cui, Hongyong
12 Gess, Benjamin
12 Wu, Fuke
12 Zhang, Jian
11 Cao, Junfei
11 Duc, Luu Hoang
11 Kühn, Christian
11 Liu, Jicheng
11 Liu, Xianbin
11 Liu, Xianming
11 Mierczyński, Janusz
11 Shen, Wenxian
11 Singer, Hermann
11 Xu, Yong
10 Chueshov, Igor’ Dmitrievich
10 Crauel, Hans
10 Liu, Qun
10 Namachchivaya, N. Sri
10 Shi, Ningzhong
10 Yang, Meihua
10 Zhu, Quanxin
9 Bates, Peter W.
9 Braumann, Carlos A.
9 Engel, Maximilian
9 Evstigneev, Igor V.
9 Feng, Chunrong
9 Haddad, Wassim Michael
9 Ji, Chunyan
9 Jiang, Jifa
9 Komori, Yoshio
9 López-de-la-Cruz, Javier
9 Ma, Qiaozhen
9 Mohammed, Salah-Eldin A.
9 Schenk-Hoppé, Klaus Reiner
9 Villafuerte, Laura
9 Wang, Ke
9 Wang, Wei
9 Xin, Jie
9 Xu, Dongmei
9 You, Yuncheng
9 Zhao, Junyilang
8 Baxendale, Peter H.
8 Blumenthal, Alex
8 Brzeźniak, Zdzisław
8 Deng, Feiqi
8 Florchinger, Patrick
8 Froyland, Gary
8 Homburg, Ale Jan
8 Josa-Fombellida, Ricardo
8 Kinra, Kush
8 Li, Ji
8 Lv, Yan
8 Mohan, Manil Thankamani
...and 3,196 more Authors
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Cited in 469 Serials

130 Journal of Differential Equations
94 Stochastics and Dynamics
89 Discrete and Continuous Dynamical Systems. Series B
83 Stochastic Analysis and Applications
76 Journal of Mathematical Analysis and Applications
58 Stochastic Processes and their Applications
55 Journal of Mathematical Physics
55 Journal of Dynamics and Differential Equations
53 Physica D
47 Journal of Statistical Physics
46 Discrete and Continuous Dynamical Systems
45 Chaos, Solitons and Fractals
45 Applied Mathematics and Computation
44 Journal of Computational and Applied Mathematics
43 Chaos
43 Communications in Nonlinear Science and Numerical Simulation
32 Nonlinearity
32 Systems & Control Letters
29 Physica A
28 Automatica
28 Proceedings of the American Mathematical Society
28 Probability Theory and Related Fields
27 The Annals of Probability
27 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
27 Nonlinear Dynamics
26 International Journal of Control
26 Mathematics and Computers in Simulation
26 Ergodic Theory and Dynamical Systems
26 Abstract and Applied Analysis
25 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
23 Computers & Mathematics with Applications
23 Mathematical Biosciences
22 Journal of Difference Equations and Applications
20 SIAM Journal on Applied Dynamical Systems
19 Journal of Functional Analysis
19 Advances in Difference Equations
18 BIT
18 Communications on Pure and Applied Analysis
17 Communications in Mathematical Physics
17 Transactions of the American Mathematical Society
16 Journal of Computational Physics
16 Physics Letters. A
16 Applied Mathematics Letters
16 Applied Mathematical Modelling
16 Mathematical Problems in Engineering
15 Mathematical Methods in the Applied Sciences
15 SIAM Journal on Control and Optimization
15 The Annals of Applied Probability
15 Dynamical Systems
14 Insurance Mathematics & Economics
14 Mathematical and Computer Modelling
14 Journal of Nonlinear Science
13 Journal of the Franklin Institute
13 Journal of Mathematical Biology
13 Bulletin of Mathematical Biology
13 Journal of Economic Dynamics & Control
13 Discrete and Continuous Dynamical Systems. Series S
13 Journal of Theoretical Biology
12 Stochastics
11 Applied Mathematics and Optimization
11 SIAM Journal on Mathematical Analysis
11 International Journal of Robust and Nonlinear Control
11 Stochastics
10 International Journal of Systems Science
10 Statistics & Probability Letters
10 Stochastic Hydrology and Hydraulics
10 Linear Algebra and its Applications
10 Stochastics and Stochastics Reports
10 Acta Mathematica Sinica. English Series
9 Physics Reports
9 Mathematische Zeitschrift
9 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
9 Acta Applicandae Mathematicae
9 Applied Numerical Mathematics
9 Journal of Theoretical Probability
9 Communications in Statistics. Theory and Methods
9 European Journal of Operational Research
9 Qualitative Theory of Dynamical Systems
9 Nonlinear Analysis. Real World Applications
8 Applicable Analysis
8 Theoretical Population Biology
8 Journal of Physics A: Mathematical and Theoretical
8 Science China. Mathematics
8 Journal of Applied Analysis and Computation
7 Journal of Mathematical Economics
7 Mathematische Nachrichten
7 Applied Mathematics and Mechanics. (English Edition)
7 MCSS. Mathematics of Control, Signals, and Systems
7 European Journal of Control
7 Journal of Inequalities and Applications
7 Journal of Nonlinear Mathematical Physics
7 Boundary Value Problems
7 Frontiers of Mathematics in China
6 Communications on Pure and Applied Mathematics
6 Journal of Approximation Theory
6 The Journal of Mathematical Sociology
6 Annals of Physics
6 Differential Equations and Dynamical Systems
6 Discrete Dynamics in Nature and Society
6 Journal of Statistical Mechanics: Theory and Experiment
...and 369 more Serials
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Cited in 56 Fields

1,588 Probability theory and stochastic processes (60-XX)
1,134 Dynamical systems and ergodic theory (37-XX)
610 Ordinary differential equations (34-XX)
589 Partial differential equations (35-XX)
426 Systems theory; control (93-XX)
335 Biology and other natural sciences (92-XX)
274 Numerical analysis (65-XX)
131 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
126 Statistics (62-XX)
116 Fluid mechanics (76-XX)
102 Statistical mechanics, structure of matter (82-XX)
63 Operator theory (47-XX)
60 Mechanics of particles and systems (70-XX)
55 Linear and multilinear algebra; matrix theory (15-XX)
50 Difference and functional equations (39-XX)
49 Mechanics of deformable solids (74-XX)
45 Geophysics (86-XX)
41 Operations research, mathematical programming (90-XX)
39 Calculus of variations and optimal control; optimization (49-XX)
38 Quantum theory (81-XX)
35 Measure and integration (28-XX)
35 Computer science (68-XX)
33 Global analysis, analysis on manifolds (58-XX)
25 Real functions (26-XX)
25 Integral equations (45-XX)
25 Information and communication theory, circuits (94-XX)
23 Functional analysis (46-XX)
22 Combinatorics (05-XX)
20 Functions of a complex variable (30-XX)
16 Classical thermodynamics, heat transfer (80-XX)
11 Approximations and expansions (41-XX)
8 General topology (54-XX)
7 Abstract harmonic analysis (43-XX)
7 Differential geometry (53-XX)
7 Relativity and gravitational theory (83-XX)
6 Topological groups, Lie groups (22-XX)
6 Manifolds and cell complexes (57-XX)
4 Number theory (11-XX)
4 Harmonic analysis on Euclidean spaces (42-XX)
3 History and biography (01-XX)
3 Several complex variables and analytic spaces (32-XX)
3 Special functions (33-XX)
3 Sequences, series, summability (40-XX)
3 Optics, electromagnetic theory (78-XX)
2 General and overarching topics; collections (00-XX)
2 Group theory and generalizations (20-XX)
2 Integral transforms, operational calculus (44-XX)
2 Algebraic topology (55-XX)
2 Astronomy and astrophysics (85-XX)
1 Mathematical logic and foundations (03-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 Algebraic geometry (14-XX)
1 Category theory; homological algebra (18-XX)
1 Geometry (51-XX)
1 Convex and discrete geometry (52-XX)
1 Mathematics education (97-XX)

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