Prolongations and stability in dynamical systems

J. Auslander; P. Seibert

Annales de l'institut Fourier (1964)

  • Volume: 14, Issue: 2, page 237-267
  • ISSN: 0373-0956

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Auslander, J., and Seibert, P.. "Prolongations and stability in dynamical systems." Annales de l'institut Fourier 14.2 (1964): 237-267. <http://eudml.org/doc/73841>.

@article{Auslander1964,
author = {Auslander, J., Seibert, P.},
journal = {Annales de l'institut Fourier},
keywords = {ordinary differential equations},
language = {eng},
number = {2},
pages = {237-267},
publisher = {Association des Annales de l'Institut Fourier},
title = {Prolongations and stability in dynamical systems},
url = {http://eudml.org/doc/73841},
volume = {14},
year = {1964},
}

TY - JOUR
AU - Auslander, J.
AU - Seibert, P.
TI - Prolongations and stability in dynamical systems
JO - Annales de l'institut Fourier
PY - 1964
PB - Association des Annales de l'Institut Fourier
VL - 14
IS - 2
SP - 237
EP - 267
LA - eng
KW - ordinary differential equations
UR - http://eudml.org/doc/73841
ER -

References

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  1. [1] J. AUSLANDER and P. SEIBERT, Prolongations and generalized Liapunov functions, Internat. Sympos. on Nonlinear Differential Equations and Nonlinear mechanics, Colorado Springs, 1961. Published: New York, London, 1963. Zbl0132.32204
  2. [2] W. H. GOTTSCHALK and G. A. HEDLUND, Topological Dynamics, Amer. Math. Soc. Colloquium Publ., Vol, XXXVI (1955). Zbl0067.15204MR17,650e
  3. [3] J. L. KELLEY, General Topology, New York, 1955. Zbl0066.16604MR16,1136c
  4. [4] J. P. LASALLE, The extent of asymptotic stability, Proc. Nat. Acad. Sci. U.S.A., 46 (1960), pp. 363-365. Zbl0094.28602MR22 #3855
  5. [5] J. P. LASALLE, Some extensions of Liapunov's second method, IRE Transactions on Circuit Theory, CT-7, 1960, pp. 520-527. 
  6. [6] S. LEFSCHETZ, Liapunov and stability in dynamical systems, Boletin Soc. Mat. Mexicana, (2) 3 (1958), pp. 25-39. Zbl0098.28901
  7. [7] I. G. MALKIN, Ob ustoĠčivosti pri postoianno deĠstvuiuščikh wozmuščeniakh, Priklad. Mat. i Mekh. 8 (1944), pp. 241-245. Zbl0061.19504
  8. [8] I. G. MALKIN, Theory of Stability of Motion, AEC-tr-3352 (1958). Original: Teoria ustoičivosti dwiženia, Gos. Izdat. Tekh. - Teoret. Lit., Moscow, 1952. 
  9. [9] P. MENDELSON, On unstable attractors, Boletin Soc. Mat. Mexicana (2) 5 (1960), pp. 270-276. Zbl0101.30301MR25 #2297
  10. [10] N. N. NEMYTSKII and N. N. STEPANOV, Qualitative Theory of Differential Equations, Princeton 1960. Original: Kačestvennaya teoria differencialnykh uravneniĠ, Moscow-Leningrad, 1947. Zbl0089.29502
  11. [11] P. SEIBERT, Ueber Stabilität unter ständig wirkenden Störungen in dynamischen Systemen, Archiv d. Math., 15, (1964) pp. 108-114. Zbl0122.09304MR29 #338
  12. [12] T. URA, Sur les courbes définies par les équations différentielles dans l'espace à m dimensions, Ann. Sci. Ecole Norm. Sup., [3] 70 (1953), pp. 287-360. Zbl0053.24702MR16,247d
  13. [13] T. URA, Sur le courant extérieur à une région invariante, Funk. Ekv., 2 (1959), pp. 143-200. Zbl0094.35602MR22 #1727
  14. [14] T. YOSHIZAWA, Liapunov's function and boundedness of solutions, Funk. Ekv., 2 (1959), pp. 95-142. Zbl0093.28005MR22 #5789
  15. [15] V. I. ZUBOV, Methods of A. M. Liapunov and their Application, AEC-tr-4439 (1961). Original: Metody A. M. Liapunova i ikh primenenie, Izdat. Léningrad. Univ. 1957. 

Citations in EuDML Documents

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  1. Andrea Bacciotti, Francesca Ceragioli, Stability and stabilization of discontinuous systems and nonsmooth Lyapunov functions
  2. Roger G. McCann, Another characterization of absolute stability
  3. Alessandra Biglio, Stabilità e stabilizzabilità di sistemi non lineari discreti
  4. Andrea Bacciotti, Francesca Ceragioli, Stability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions
  5. Marco Sabatini, Hopf bifurcation from infinity
  6. M. L. Bertotti, V. Moauro, Bifurcation and total stability
  7. Roger C. McCann, On absolute stability

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