Menu
![](/uploads/1/2/5/6/125668585/100606203.jpeg)
A differential equation can possess a stationary point. For example, for the equation, the stationary solution is, which is obtained for the initial condition. Beginning with another initial condition, the solution y ( t ) tends toward the stationary point, but reaches it only at the limit of infinite time, so the uniqueness of solutions (over all finite times) is guaranteed.
Universitext Authors: Arnold, Vladimir I.
Buy this book
Buy Softcover
- ISBN 978-3-540-34563-3
- Free shipping for individuals worldwide
- Usually dispatched within 3 to 5 business days.
- The final prices may differ from the prices shown due to specifics of VAT rules
From the reviews: '... This book is an excellent text for a course whose goal is a mathematical treatment of differential equations and the related physical systems.' L'Enseignment Mathematique '... Arnold's book is unique as a sophisticated but accessible introduction to the modern theory, and we should be grateful that it exists in a convenient language.' Mathematical Association of America Monthly
From the reviews:
'Professor Arnold has expanded his classic book to include new material on exponential growth, predator-prey, the pendulum, impulse response, symmetry groups and group actions, perturbation and bifurcation … . The new edition is highly recommended as a general reference for the essential theory of ordinary differential equations and as a textbook for an introductory course for serious undergraduate or graduate students. … In the US system, it is an excellent text for an introductory graduate course.' (Carmen Chicone, SIAM Review, Vol. 49 (2), 2007)
'Vladimir Arnold’s is a master, not just of the technical realm of differential equations but of pedagogy and exposition as well. … The writing throughout is crisp and clear. … Arnold’s says that the book is based on a year-long sequence of lectures for second-year mathematics majors in Moscow. In the U.S., this material is probably most appropriate for advanced undergraduates or first-year graduate students.' (William J. Satzer, MathDL, August, 2007)
Buy this book
Buy Softcover
- ISBN 978-3-540-34563-3
- Free shipping for individuals worldwide
- Usually dispatched within 3 to 5 business days.
- The final prices may differ from the prices shown due to specifics of VAT rules
Services for this Book
Recommended for you
Bibliographic Information
- Vladimir I. Arnold
- Softcover ISBN
- 978-3-540-34563-3
- Series ISSN
- 0172-5939
- Edition Number
- 1
![Vladimir Vladimir](http://ecx.images-amazon.com/images/I/41xl0nCW5OL.jpg)
- Number of Pages
- IV, 338
- Number of Illustrations
- 272 b/w illustrations
- Additional Information
- Original Russion edition published by Nauka, Moscow, 1984
- Topics
- Volume 2, Number 3 (1980), 514-522.
Review: V. I. Arnold, Ordinary differential equations
More by Martin Braun
Search this author in:
Article information
Source
Bull. Amer. Math. Soc. (N.S.), Volume 2, Number 3 (1980), 514-522.
Bull. Amer. Math. Soc. (N.S.), Volume 2, Number 3 (1980), 514-522.
Dates
First available in Project Euclid: 4 July 2007
First available in Project Euclid: 4 July 2007
Permanent link to this document
https://projecteuclid.org/euclid.bams/1183546372
https://projecteuclid.org/euclid.bams/1183546372
Citation
Braun, Martin. Review: V. I. Arnold, Ordinary differential equations. Bull. Amer. Math. Soc. (N.S.) 2 (1980), no. 3, 514--522. https://projecteuclid.org/euclid.bams/1183546372
Format:
Delivery Method:
DownloadEmailEmail sent.
References
- 1. S. Bancroft, J. K. Hale and D. Sweet, Alternative problems for nonlinear functional equations, J. Differential Equations 4 (1968), 40-56.Zentralblatt MATH: 0159.20001
Mathematical Reviews (MathSciNet): MR220118
Digital Object Identifier: doi:10.1016/0022-0396(68)90047-8 - 2. N. Chafee and E. F. Infante, A bifurcation problem for a nonlinear partial differential equation of parabolic type, C.D.S. Tech. Rep. 74-5, Lefschetz Center for Dynamical Systems, Brown Univ., 1974.Zentralblatt MATH: 0296.35046
Mathematical Reviews (MathSciNet): MR440205
Digital Object Identifier: doi:10.1080/00036817408839081 - 3. N. Chafee, Behavior of solutions leaving the neighborhood of a saddle point for a nonlinear evolution equation, J. Math. Anal. Appl. 58 (1977), 312-325.Zentralblatt MATH: 0348.34047
Mathematical Reviews (MathSciNet): MR445080
Digital Object Identifier: doi:10.1016/0022-247X(77)90209-8 - 4. C. C. Conley and R. Easton, Isolated invariant sets and isolating blocks. Trans. Amer. Math. Soc. 158 (1971), 35-61.Zentralblatt MATH: 0223.58011
Mathematical Reviews (MathSciNet): MR279830
Digital Object Identifier: doi:10.1090/S0002-9947-1971-0279830-1 - 5. R. Easton, Regularization of vector fields by surgery, J. Differential Equations 10 (1971) 92-99.Zentralblatt MATH: 0215.28402
Mathematical Reviews (MathSciNet): MR315741
Digital Object Identifier: doi:10.1016/0022-0396(71)90098-2 - 6. H. Furstenberg, Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions, J. Analyse Math. 31 (1977), 204-256.Zentralblatt MATH: 0347.28016
Mathematical Reviews (MathSciNet): MR498471
Digital Object Identifier: doi:10.1007/BF02813304 - 7. H. Furstenberg and B. Weiss, Topological dynamics and combinatorial number theory, J. Analyse Math. 34 (1978), 61-85.Zentralblatt MATH: 0425.54023
Mathematical Reviews (MathSciNet): MR531271
Digital Object Identifier: doi:10.1007/BF02790008 - 8. H. Furstenberg and Y. Katznelson, An ergodic Szemerédi theorem for commuting transformations, J. Analyze Math. 34 (1978), 275-291.Zentralblatt MATH: 0426.28014
Mathematical Reviews (MathSciNet): MR531279
Digital Object Identifier: doi:10.1007/BF02790016 - 9. J. K. Hale, Dynamical systems and stability, J. Math. Anal. Appl. 26 (1969), 39-59.Zentralblatt MATH: 0179.13303
Mathematical Reviews (MathSciNet): MR244582
Digital Object Identifier: doi:10.1016/0022-247X(69)90175-9 - 10. J. P. LaSalle, An invariance principle in the theory of stability, Int. Symp. on Diff. Eqs. and Dyn. Systems, J. K. Hale and J. P. LaSalle (eds.), Academic Press, New York, 1967, p. 277.Zentralblatt MATH: 0183.09401
Mathematical Reviews (MathSciNet): MR226132 - 11. A. Liapunov, Problème général de la stabilité du mouvement, Ann. Sci. Toulouse 2 (1907), 203-474.
- 12. B. J. Matkowsky, A simple nonlinear dynamic stability problem, Bull. Amer. Math. Soc. 76 (1970), 620-625.Zentralblatt MATH: 0195.11102
Mathematical Reviews (MathSciNet): MR257544
Digital Object Identifier: doi:10.1090/S0002-9904-1970-12461-2
Project Euclid: euclid.bams/1183531825 - 13. J. Moser, Periodic orbits near an equilibrium and a theorem by A. Weinstein, Comm. Pure Appl. Math. 29 (1976), 727-747.Zentralblatt MATH: 0346.34024
Mathematical Reviews (MathSciNet): MR426052
Digital Object Identifier: doi:10.1002/cpa.3160290613 - 14. C. C. Pugh, On a theorem of P. Hartman, Amer. J. Math. 91 (1969), 363-369.Zentralblatt MATH: 0197.20701
Mathematical Reviews (MathSciNet): MR257533
Digital Object Identifier: doi:10.2307/2373513 - 15. J. Roels, An extension to resonant case of Liapunov's theorem concerning the periodic solutions near a Hamiltonian equilibrium, J. Differential Equations 9 (1971), 300-324.Zentralblatt MATH: 0245.70022
Mathematical Reviews (MathSciNet): MR273155
Digital Object Identifier: doi:10.1016/0022-0396(71)90084-2 - 16. J. Roels, Families of periodic solutions near a Hamiltonian equilibrium when the ratio of 2 eigenvalues is 3, J. Differential Equations 10 (1971), 431-447.Zentralblatt MATH: 0226.34038
Mathematical Reviews (MathSciNet): MR294789
Digital Object Identifier: doi:10.1016/0022-0396(71)90005-2 - 17. D. S. Schmidt and D. Sweet, A unifying theory in determining periodic families for Hamiltonian systems at resonance, Tech. Rep. TR 73-3, Univ. of Maryland, 1973.Zentralblatt MATH: 0275.34043
Mathematical Reviews (MathSciNet): MR328221
Digital Object Identifier: doi:10.1016/0022-0396(73)90070-3 - 18. C. L. Siegel and J. Moser, Lectures on celestial mechanics, Springer-Verlag, New York, 1971.Zentralblatt MATH: 0312.70017
Mathematical Reviews (MathSciNet): MR502448 - 19. A. Weinstein, Lagrangian submanifolds and Hamiltonian systems, Ann. Math. 98 (1973), 377-410.Zentralblatt MATH: 0271.58008
Mathematical Reviews (MathSciNet): MR331428
Digital Object Identifier: doi:10.2307/1970911 - 20. A. Weinstein, Normal modes for nonlinear Hamiltonian systems, Invent. Math. 20 (1973), 47-57.Zentralblatt MATH: 0264.70020
Mathematical Reviews (MathSciNet): MR328222
Digital Object Identifier: doi:10.1007/BF01405263
![](/uploads/1/2/5/6/125668585/100606203.jpeg)