Gew¨ohnliche Differentialgleichungen und Dynamische Systeme

Gew¨ohnliche Differentialgleichungen und Dynamische Systeme Gew¨ohnliche Differentialgleichungen und Dynamische Systeme

19.11.2013 Aufrufe

Literatur [Ama83] Herbert Amann. Gewöhnliche Differentialgleichungen. de Gruyter Lehrbuch. [de Gruyter Textbook]. Walter de Gruyter & Co., Berlin, 1983. [Arn73] [Arn91] [CG93] [CH82] [CL55] [DB94] [Dev89] [GH83] [GS85] Ludwig Arnold. Stochastische Differentialgleichungen. R. Oldenbourg Verlag, Munich, 1973. Theorie und Anwendung. V.I. Arnol’d. Gewoehnliche Differentialgleichungen. Hochschulbuecher fuer Mathematik, 83. Berlin: Deutscher Verlag der Wissenschaften., 1991. Lennart Carleson and Theodore W. Gamelin. Complex dynamics. Universitext: Tracts in Mathematics. Springer-Verlag, 1993. Shui Nee Chow and Jack K. Hale. Methods of bifurcation theory, volume 251 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science]. Springer-Verlag, New York, 1982. E. A. Coddington and N. Levinson. Theory of ordinary differential equations. New York, Toronto, London: McGill-Hill Book Company, Inc. XII, 1955. Peter Deuflhard and Folkmar Bornemann. Numerische Mathematik. II. de Gruyter Lehrbuch. [de Gruyter Textbook]. Walter de Gruyter & Co., Berlin, 1994. Integration gewöhnlicher Differentialgleichungen. [Integration of ordinary differential equations]. Robert L. Devaney. An introduction to chaotic dynamical systems. Addison-Wesley Publishing Company, 1989. J. Guckenheimer and Ph. Holmes. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Applied Mathematical Sciences, 42, Springer, New York, 1983. Martin Golubitsky and David G. Schaeffer. Singularities and groups in bifurcation theory. Vol. I, volume 51 of Applied Mathematical Sciences. Springer-Verlag, New York, 1985. [GSS88] Martin Golubitsky, Ian Stewart, and David G. Schaeffer. Singularities and groups in bifurcation theory. Vol. II, volume 69 of Applied Mathematical Sciences. Springer- Verlag, New York, 1988. [Hal88] [Hen81] Jack K. Hale. Asymptotic behavior of dissipative systems, volume 25 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 1988. D. Henry. Geometric Theory of Semilinear Parabolic Equations. Springer Lecture Notes in Mathematics, Vol. 840, 1981. 98

[Ise96] [Kel67] [KK74] [Kre85] Arieh Iserles. A first course in the numerical analysis of differential equations. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge, 1996. A. Kelley. The stable, center-stable, center-unstable, unstable manifolds. J. Diff. Eq., 3:546–570, 1967. H. W. Knobloch and F. Kappel. Gewöhnliche Differentialgleichungen. B. G. Teubner, Stuttgart, 1974. Mathematische Leitfäden. Ulrich Krengel. Ergodic theorems. De Gruyter Studies in Mathematics 6. Berlin-New York: Walter de Gruyter. VIII, 1985. [Lor63] E.N. Lorenz. Deterministic non-periodic flow. J. Atmos. Sci., 1963. [Man91] Benoit B. Mandelbrot. Die fraktale Geometrie der Natur. Birkhaeuser, 1991. [Mil99] John Milnor. Dynamics in one complex variable. Introductory lectures. Vieweg., 1999. [Oks98] Bernt Oksendal. Stochastic differential equations. Universitext. Springer-Verlag, Berlin, fifth edition, 1998. An introduction with applications. [Pal82] [Pea90] [PR86] [RT71] Welington Palis, Jacob jun.; de Melo. Geometric theory of dynamical systems. An introduction. Springer-Verlag, 1982. G. Peano. Démonstration de l’integrabilité des équations différentielles ordinaires. Math. Annal., 37, 1890. H.-O. Peitgen and P.H. Richter. The beauty of fractals. Images of complex dynamical systems. Springer-Verlag, 1986. David Ruelle and Floris Takens. On the nature of turbulence. Commun. Math. Phys., 20:167–192, 1971. [SH96] A. M. Stuart and A. R. Humphries. Dynamical systems and numerical analysis, volume 2 of Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, Cambridge, 1996. [Sil65] L. P. Sil’nikov. A case of the existence of a denumerable set of periodic motions. Dokl. Akad. Nauk SSSR, 160:558–561, 1965. [SU03] G. Schneider and H. Uecker. Chaos und Fraktale, Vorlesungsskript, WS 2002/2003. 2003. [Tem97] Roger Temam. Infinite-dimensional dynamical systems in mechanics and physics, volume 68 of Applied Mathematical Sciences. Springer-Verlag, New York, second edition, 1997. 99

[Ise96]<br />

[Kel67]<br />

[KK74]<br />

[Kre85]<br />

Arieh Iserles. A first course in the numerical analysis of differential equations. Cambridge<br />

Texts in Applied Mathematics. Cambridge University Press, Cambridge, 1996.<br />

A. Kelley. The stable, center-stable, center-unstable, unstable manifolds. J. Diff. Eq.,<br />

3:546–570, 1967.<br />

H. W. Knobloch and F. Kappel. Gewöhnliche <strong>Differentialgleichungen</strong>. B. G. Teubner,<br />

Stuttgart, 1974. Mathematische Leitfäden.<br />

Ulrich Krengel. Ergodic theorems. De Gruyter Studies in Mathematics 6. Berlin-New<br />

York: Walter de Gruyter. VIII, 1985.<br />

[Lor63] E.N. Lorenz. Deterministic non-periodic flow. J. Atmos. Sci., 1963.<br />

[Man91] Benoit B. Mandelbrot. Die fraktale Geometrie der Natur. Birkhaeuser, 1991.<br />

[Mil99]<br />

John Milnor. Dynamics in one complex variable. Introductory lectures. Vieweg.,<br />

1999.<br />

[Oks98] Bernt Oksendal. Stochastic differential equations. Universitext. Springer-Verlag,<br />

Berlin, fifth edition, 1998. An introduction with applications.<br />

[Pal82]<br />

[Pea90]<br />

[PR86]<br />

[RT71]<br />

Welington Palis, Jacob jun.; de Melo. Geometric theory of dynamical systems. An<br />

introduction. Springer-Verlag, 1982.<br />

G. Peano. Démonstration de l’integrabilité des équations différentielles ordinaires.<br />

Math. Annal., 37, 1890.<br />

H.-O. Peitgen and P.H. Richter. The beauty of fractals. Images of complex dynamical<br />

systems. Springer-Verlag, 1986.<br />

David Ruelle and Floris Takens. On the nature of turbulence. Commun. Math. Phys.,<br />

20:167–192, 1971.<br />

[SH96] A. M. Stuart and A. R. Humphries. Dynamical systems and numerical analysis,<br />

volume 2 of Cambridge Monographs on Applied and Computational Mathematics.<br />

Cambridge University Press, Cambridge, 1996.<br />

[Sil65]<br />

L. P. Sil’nikov. A case of the existence of a denumerable set of periodic motions.<br />

Dokl. Akad. Nauk SSSR, 160:558–561, 1965.<br />

[SU03] G. Schneider and H. Uecker. Chaos <strong>und</strong> Fraktale, Vorlesungsskript, WS 2002/2003.<br />

2003.<br />

[Tem97] Roger Temam. Infinite-dimensional dynamical systems in mechanics and physics,<br />

volume 68 of Applied Mathematical Sciences. Springer-Verlag, New York, second<br />

edition, 1997.<br />

99

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