Arnold, L. Behavior of Kreiss bounded \(C_0\)-semigroups on a Hilbert space. (English) Zbl 1509.47063 Adv. Oper. Theory 7, No. 4, Paper No. 62, 7 p. (2022). MSC: 47D06 34D05 35B45 35L05 PDFBibTeX XMLCite \textit{L. Arnold}, Adv. Oper. Theory 7, No. 4, Paper No. 62, 7 p. (2022; Zbl 1509.47063) Full Text: DOI arXiv
Arnold, Ludwig; Chueshov, Igor; Ochs, Gunter Random dynamical systems methods in ship stability: a case study. (English) Zbl 1092.34028 Deuschel, Jean-Dominique (ed.) et al., Interacting stochastic systems. Berlin: Springer (ISBN 3-540-23033-5/hbk). 409-433 (2005). Reviewer: Henri Schurz (Carbondale) MSC: 34F05 37H10 37H15 37H20 60H10 70L05 93E15 34C60 PDFBibTeX XMLCite \textit{L. Arnold} et al., in: Interacting stochastic systems. Berlin: Springer. 409--433 (2005; Zbl 1092.34028)
Arnold, L.; Imkeller, P.; Namachchivaya, N. Sri The asymptotic stability of a noisy non-linear oscillator. (English) Zbl 1236.70044 J. Sound Vib. 269, No. 3-5, 1003-1029 (2004). MSC: 70L05 60H40 34D20 34F05 70K20 PDFBibTeX XMLCite \textit{L. Arnold} et al., J. Sound Vib. 269, No. 3--5, 1003--1029 (2004; Zbl 1236.70044) Full Text: DOI
Arnold, Ludwig Linear and nonlinear diffusion approximation of the slow motion in systems with two time scales. (English) Zbl 1079.34046 Sri Namachchivaya, N. (ed.) et al., IUTAM symposium on nonlinear stochastic dynamics. Proceedings of the IUTAM symposium, Monticello, IL, USA, Augsut 26–30, 2002. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-1471-6/hbk). Solid Mech. Appl. 110, 5-18 (2003). Reviewer: Barbara Gentz (Berlin) MSC: 34F05 34E15 34C29 60J60 34C23 PDFBibTeX XMLCite \textit{L. Arnold}, Solid Mech. Appl. 110, 5--18 (2003; Zbl 1079.34046) Full Text: DOI
Arnold, Ludwig; Chueshov, Igor Cooperative random and stochastic differential equations. (English) Zbl 1017.37026 Discrete Contin. Dyn. Syst. 7, No. 1, 1-33 (2001). Reviewer: Vigirdas Mackevičius (Vilnius) MSC: 37H10 34F05 60H10 47B80 93E15 PDFBibTeX XMLCite \textit{L. Arnold} and \textit{I. Chueshov}, Discrete Contin. Dyn. Syst. 7, No. 1, 1--33 (2001; Zbl 1017.37026) Full Text: DOI
Arnold, Ludwig; Schmalfuss, Björn Lyapunov’s second method for random dynamical systems. (English) Zbl 1040.37035 J. Differ. Equations 177, No. 1, 235-265 (2001). MSC: 37H10 34D20 34F05 60H10 PDFBibTeX XMLCite \textit{L. Arnold} and \textit{B. Schmalfuss}, J. Differ. Equations 177, No. 1, 235--265 (2001; Zbl 1040.37035) Full Text: DOI
Arnold, Ludwig Hasselmann’s program revisited: The analysis of stochasticity in deterministic climate models. (English) Zbl 1015.34037 Imkeller, Peter (ed.) et al., Stochastic climate models. Proceedings of a workshop, Chorin, Germany, Summer 1999. Basel: Birkhäuser. Prog. Probab. 49, 141-157 (2001). Reviewer: Jozef Myjak (L’Aquila) MSC: 34C29 86A10 34F05 60H10 60F05 60F10 34D45 34C60 PDFBibTeX XMLCite \textit{L. Arnold}, Prog. Probab. 49, 141--157 (2001; Zbl 1015.34037)
Arnold, Ludwig; Chueshov, Igor A limit set trichotomy for order-preserving random systems. (English) Zbl 0997.34044 Positivity 5, No. 2, 95-114 (2001). Reviewer: V.Wihstutz (Charlotte) MSC: 34F05 34D09 37H05 47B80 60H25 93E15 34D45 PDFBibTeX XMLCite \textit{L. Arnold} and \textit{I. Chueshov}, Positivity 5, No. 2, 95--114 (2001; Zbl 0997.34044) Full Text: DOI
Arnold, Ludwig; Imkeller, Peter Rotation numbers for linear stochastic differential equations. (English) Zbl 0944.60065 Ann. Probab. 27, No. 1, 130-149 (1999). Reviewer: R.Buckdahn (Brest) MSC: 60H10 34D08 60H07 PDFBibTeX XMLCite \textit{L. Arnold} and \textit{P. Imkeller}, Ann. Probab. 27, No. 1, 130--149 (1999; Zbl 0944.60065) Full Text: DOI
Arnold, Ludwig Random dynamical systems. (English) Zbl 0906.34001 Springer Monographs in Mathematics. Berlin: Springer. xi, 586 p. (1998). Reviewer: Henri Schurz (Bogotá) MSC: 34-02 34F05 60H10 37Hxx 37-02 37H05 37H10 37H15 37H20 93E15 PDFBibTeX XMLCite \textit{L. Arnold}, Random dynamical systems. Berlin: Springer (1998; Zbl 0906.34001)
Arnold, Ludwig; Imkeller, Peter Normal forms for stochastic differential equations. (English) Zbl 0906.60048 Probab. Theory Relat. Fields 110, No. 4, 559-588 (1998). MSC: 60H10 34F05 37A99 93E03 PDFBibTeX XMLCite \textit{L. Arnold} and \textit{P. Imkeller}, Probab. Theory Relat. Fields 110, No. 4, 559--588 (1998; Zbl 0906.60048) Full Text: DOI
Arnold, L.; Doyle, M. M.; Sri Namachchivaya, N. Small noise expansion of moment Lyapunov exponents for two-dimensional systems. (English) Zbl 0890.60055 Dyn. Stab. Syst. 12, No. 3, 187-211 (1997). Reviewer: René L.Schilling (Erlangen) MSC: 60H10 34F05 93E15 PDFBibTeX XMLCite \textit{L. Arnold} et al., Dyn. Stab. Syst. 12, No. 3, 187--211 (1997; Zbl 0890.60055) Full Text: DOI
Arnold, Ludwig; Eizenberg, Alex; Wihstutz, Volker Large noise asymptotics of invariant measures, with applications to Lyapunov exponents. (English) Zbl 0869.93051 Stochastics Stochastics Rep. 59, No. 1-2, 71-142 (1996). Reviewer: B.L.S.Prakasa Rao (New Delhi) MSC: 93E15 34D08 34F05 60H10 PDFBibTeX XMLCite \textit{L. Arnold} et al., Stochastics Stochastics Rep. 59, No. 1--2, 71--142 (1996; Zbl 0869.93051) Full Text: DOI
Arnold, Ludwig; Kloeden, Peter Discretization of a random dynamical system near a hyperbolic point. (English) Zbl 0857.34058 Math. Nachr. 181, 43-72 (1996). Reviewer: M.D.Lax (Long Beach) MSC: 34F05 65C99 34D08 65L05 93E15 PDFBibTeX XMLCite \textit{L. Arnold} and \textit{P. Kloeden}, Math. Nachr. 181, 43--72 (1996; Zbl 0857.34058) Full Text: DOI
Arnold, Ludwig; Imkeller, Peter Stratonovich calculus with spatial parameters and anticipative problems in multiplicative ergodic theory. (English) Zbl 0847.60037 Stochastic Processes Appl. 62, No. 1, 19-54 (1996). MSC: 60H10 34F05 37A99 60G17 PDFBibTeX XMLCite \textit{L. Arnold} and \textit{P. Imkeller}, Stochastic Processes Appl. 62, No. 1, 19--54 (1996; Zbl 0847.60037) Full Text: DOI
Arnold, Ludwig; Namachchivaya, N. Sri; Schenk-Hoppé, Klaus R. Toward an understanding of stochastic Hopf bifurcation: a case study. (English) Zbl 1298.37038 Int. J. Bifurcation Chaos Appl. Sci. Eng. 6, No. 11, 1947-1975 (1996). MSC: 37H10 37H20 34F10 PDFBibTeX XMLCite \textit{L. Arnold} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 6, No. 11, 1947--1975 (1996; Zbl 1298.37038) Full Text: DOI
Doyle, M. M.; Sri Namachchivaya, N.; Arnold, L. Small noise expansion of moment Lyapunov exponents for two-dimensional systems. (English) Zbl 1005.37507 Naess, A. (ed.) et al., Advances in nonlinear stochastic mechanics. Proceedings of the IUTAM symposium. Trondheim, Norway, 3-7 July 1995. Dordrecht: Kluwer Academic Publishers. Solid Mech. Appl. 47, 153-168 (1996). MSC: 37H15 60H10 34F05 34D08 70L05 PDFBibTeX XMLCite \textit{M. M. Doyle} et al., Solid Mech. Appl. 47, 153--168 (1996; Zbl 1005.37507)
Arnold, L.; Schmalfuss, B. Fixed points and attractors for random dynamical systems. (English) Zbl 0925.58050 Naess, A. (ed.) et al., Advances in nonlinear stochastic mechanics. Proceedings of the IUTAM symposium. Trondheim, Norway, 3–7 July 1995. Dordrecht: Kluwer Academic Publishers. Solid Mech. Appl. 47, 19-28 (1996). MSC: 37C70 70L05 34D45 34F05 PDFBibTeX XMLCite \textit{L. Arnold} and \textit{B. Schmalfuss}, Solid Mech. Appl. 47, 19--28 (1996; Zbl 0925.58050)
Arnold, Ludwig Anticipative problems in the theory of random dynamical systems. (English) Zbl 0821.60062 Cranston, Michael C. (ed.) et al., Stochastic analysis. Proceedings of the Summer Research Institute on stochastic analysis, held at Cornell University, Ithaca, NY, USA, July 11-30, 1993. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 57, 529-541 (1995). MSC: 60H10 34F05 PDFBibTeX XMLCite \textit{L. Arnold}, Proc. Symp. Pure Math. 57, 529--541 (1995; Zbl 0821.60062)
Arnold, Ludwig; Xu, Kedai Normal forms for random differential equations. (English) Zbl 0820.34037 J. Differ. Equations 116, No. 2, 484-503 (1995). Reviewer: C.A.Braumann (Evora) MSC: 34F05 34C20 60H10 PDFBibTeX XMLCite \textit{L. Arnold} and \textit{K. Xu}, J. Differ. Equations 116, No. 2, 484--503 (1995; Zbl 0820.34037) Full Text: DOI
Arnold, Ludwig; Gundlach, Volker Matthias; Demetrius, Lloyd Evolutionary formalism for products of positive random matrices. (English) Zbl 0818.15015 Ann. Appl. Probab. 4, No. 3, 859-901 (1994). Reviewer: H.Crauel (Saarbrücken) MSC: 15B52 15B48 34D08 92D15 PDFBibTeX XMLCite \textit{L. Arnold} et al., Ann. Appl. Probab. 4, No. 3, 859--901 (1994; Zbl 0818.15015) Full Text: DOI
Arnold, L. Random dynamical systems. (Zufällige dynamische Systeme.) (German) Zbl 0805.60048 Jahresber. Dtsch. Math.-Ver. 96, No. 3, 85-100 (1994). Reviewer: W.Kliemann (Ames) MSC: 60H10 34D08 34F05 93E03 PDFBibTeX XMLCite \textit{L. Arnold}, Jahresber. Dtsch. Math.-Ver. 96, No. 3, 85--100 (1994; Zbl 0805.60048)
Arnold, Ludwig; Xu, Kedai Simultaneous normal form and center manifold reduction for random differential equations. (English) Zbl 0938.60512 Perelló, C. (ed.) et al., International conference on differential equations. Vol. 1, 2. Proceedings of the conference, EQUADIFF 91, Barcelona, Spain, August 26-31, 1991. Singapore: World Scientific. 68-80 (1993). MSC: 60H10 34C20 34F05 PDFBibTeX XMLCite \textit{L. Arnold} and \textit{K. Xu}, in: International conference on differential equations. Vol. 1, 2. Proceedings of the conference, EQUADIFF 91, Barcelona, Spain, August 26-31, 1991. Singapore: World Scientific. 68--80 (1993; Zbl 0938.60512)
Arnold, Ludwig; Xu, Kedai Normal forms for random diffeomorphisms. (English) Zbl 0763.34026 J. Dyn. Differ. Equations 4, No. 3, 445-483 (1992). Reviewer: R.Mikulevičius (Vilnius) MSC: 34C20 34F05 37-XX 34D08 60H10 PDFBibTeX XMLCite \textit{L. Arnold} and \textit{K. Xu}, J. Dyn. Differ. Equations 4, No. 3, 445--483 (1992; Zbl 0763.34026) Full Text: DOI
Arnold, Ludwig (ed.); Crauel, Hans (ed.); Eckmann, Jean-Pierre (ed.) Lyapunov exponents. Proceedings of a conference, held in Oberwolfach, Germany, May 28-June 2, 1990. (English) Zbl 0733.00015 Lecture Notes in Mathematics, 1486. Berlin etc.: Springer-Verlag. vi, 365 p. DM 70.00 (1991). MSC: 00B25 58-06 34-06 93-06 60-06 PDFBibTeX XML Full Text: DOI
Arnold, Ludwig; Boxler, Petra Additive noise turns a hyperbolic fixed point into a stationary solution. (English) Zbl 0741.34010 Lyapunov exponents, Proc. Conf., Oberwolfach/Ger. 1990, Lect. Notes Math. 1486, 159-164 (1991). Reviewer: A.Dale (Durban) MSC: 34C05 34D05 34F05 34D08 PDFBibTeX XMLCite \textit{L. Arnold} and \textit{P. Boxler}, Lect. Notes Math. None, 159--164 (1991; Zbl 0741.34010)
Arnold, L. Stabilization by noise revisited. (English) Zbl 0765.93076 Z. Angew. Math. Mech. 70, No. 7, 235-246 (1990). Reviewer: Leslaw Socha (Zabrze) MSC: 93E15 60H10 93C05 34D08 PDFBibTeX XMLCite \textit{L. Arnold}, Z. Angew. Math. Mech. 70, No. 7, 235--246 (1990; Zbl 0765.93076) Full Text: DOI
Arnold, L. Towards a theory of nonlinear stochastic systems. (English) Zbl 0694.34034 Applications of mathematics in industry and technology, Proc. 3rd Ger./Ital. Symp., Siena/Italy 1988, 248-258 (1989). MSC: 37-XX 34F05 34A34 PDFBibTeX XML
Arnold, Ludwig; Kloeden, Peter Lyapunov exponents and rotation number of two-dimensional systems with telegraphic noise. (English) Zbl 0684.60046 SIAM J. Appl. Math. 49, No. 4, 1242-1274 (1989). Reviewer: G.Kersting MSC: 60H10 34F05 93E15 PDFBibTeX XMLCite \textit{L. Arnold} and \textit{P. Kloeden}, SIAM J. Appl. Math. 49, No. 4, 1242--1274 (1989; Zbl 0684.60046) Full Text: DOI
Arnold, Ludwig; San Martin, Luiz A multiplicative ergodic theorem for rotation numbers. (English) Zbl 0684.34059 J. Dyn. Differ. Equations 1, No. 1, 95-119 (1989). MSC: 34F05 37A99 60G10 60F15 PDFBibTeX XMLCite \textit{L. Arnold} and \textit{L. San Martin}, J. Dyn. Differ. Equations 1, No. 1, 95--119 (1989; Zbl 0684.34059) Full Text: DOI
Arnold, Ludwig; Boxler, Petra Eigenvalues, bifurcation, and center manifolds in the presence of noise. (English) Zbl 0681.60055 Differential equations, Proc. EQUADIFF Conf., Xanthi/Greece 1987, Lect. Notes Pure Appl. Math. 118, 33-48 (1989). Reviewer: D.Bobrowski MSC: 60H25 34F05 PDFBibTeX XML
Arnold, Ludwig; Papanicolaou, George; Wihstutz, Volker Asymptotic analysis of the Lyapunov exponent and rotation number of the random oscillator and applications. (English) Zbl 0603.60051 SIAM J. Appl. Math. 46, 427-450 (1986). Reviewer: W.Rümelin MSC: 60H10 60J99 34F05 70L05 93E15 PDFBibTeX XMLCite \textit{L. Arnold} et al., SIAM J. Appl. Math. 46, 427--450 (1986; Zbl 0603.60051) Full Text: DOI
Arnold, Ludwig; Wihstutz, Volker Lyapunov exponents: A survey. (English) Zbl 0599.60061 Lyapunov exponents, Proc. Workshop, Bremen/Ger. 1984, Lect. Notes Math. 1186, 1-26 (1986). Reviewer: Y.Kifer MSC: 60H25 34F05 93E15 28D05 37A99 PDFBibTeX XML
Arnold, L.; Horsthemke, W.; Stuckl, J. W. The influence of external real and white noise on the Lotka-Volterra model. (English) Zbl 0433.92019 Biom. J. 21, 451-471 (1979). MSC: 92D25 60G10 60G12 34A34 PDFBibTeX XMLCite \textit{L. Arnold} et al., Biom. J. 21, 451--471 (1979; Zbl 0433.92019) Full Text: DOI
Arnold, Ludwig; Wihstutz, Volker On the stability and growth of real noise parameter-excited linear systems. (English) Zbl 0392.93039 Measure Theory Appl. stoch. Anal., Proc. Oberwolfach Conf. 1977, Lect. Notes Math. 695, 211-227 (1978). MSC: 93E15 60G10 34F05 PDFBibTeX XML
Arnold, Ludwig Stochastische Differentialgleichungen. Theorie und Anwendung. (German) Zbl 0266.60039 München-Wien: R. Oldenbourg Verlag. 239 S. mit 10 Abb. DM 65.00 (1973). MSC: 60-01 60H10 93Exx 34F05 PDFBibTeX XML