Geodesic
Nonexpansive Uniformly Asymptotically Stable Flows are Linear
Canadian mathematical bulletin, Tome 24 (1981) no. 4, pp. 401-407

Voir la notice de l'article provenant de la source Cambridge University Press

We show that if a flow (R, X, π) on a separable metric space (X, d) satisfies (i) the transition mapping π(t, •): X → X is non-expansive for every t ≥ 0; (ii) X contains a globally uniformly asymptotically stable compact invariant subset, then the flow (R, X, π) is linear in the sense that it can be topologically and equivariantly embedded into a flow () on the Hilbert space l2 for which all of the transition mappings are linear operators on l2. 
Janos, Ludvik; McCann, Roger C.; Solomon, J. L. Nonexpansive Uniformly Asymptotically Stable Flows are Linear. Canadian mathematical bulletin, Tome 24 (1981) no. 4, pp. 401-407. doi: 10.4153/CMB-1981-062-4
@article{10_4153_CMB_1981_062_4,
     author = {Janos, Ludvik and McCann, Roger C. and Solomon, J. L.},
     title = {Nonexpansive {Uniformly} {Asymptotically} {Stable} {Flows} are {Linear}},
     journal = {Canadian mathematical bulletin},
     pages = {401--407},
     year = {1981},
     volume = {24},
     number = {4},
     doi = {10.4153/CMB-1981-062-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-062-4/}
}
TY  - JOUR
AU  - Janos, Ludvik
AU  - McCann, Roger C.
AU  - Solomon, J. L.
TI  - Nonexpansive Uniformly Asymptotically Stable Flows are Linear
JO  - Canadian mathematical bulletin
PY  - 1981
SP  - 401
EP  - 407
VL  - 24
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-062-4/
DO  - 10.4153/CMB-1981-062-4
ID  - 10_4153_CMB_1981_062_4
ER  - 
%0 Journal Article
%A Janos, Ludvik
%A McCann, Roger C.
%A Solomon, J. L.
%T Nonexpansive Uniformly Asymptotically Stable Flows are Linear
%J Canadian mathematical bulletin
%D 1981
%P 401-407
%V 24
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-062-4/
%R 10.4153/CMB-1981-062-4
%F 10_4153_CMB_1981_062_4

[1] 1. Baayen, P. C. and de Groot, J., Linearization of Locally Compact Transformation Groups in Hilbert Space. Math. Systems Theory, Vol. 2 No. 4, 363-379. Google Scholar

[2] 2. Bhatia, N. P. and Szegö, G. P., Dynamical systems: Stability Theory and Applications, Lecture Notes in Math. 35, Springer Verlag, Berlin, 1967. Google Scholar

[3] 3. Edelstein, Michael, On the Homomorphic and Isomorphic Embeddings of a Semiflow into a Radial Flow. Pacific J. Math.. 91 (1980) 281-291. Google Scholar

[4] 4. Janos, Ludvik, On Representation of Self-mappings. Proc. Amer. Math. Soc. 26 (1980), 529-533. Google Scholar

[5] 5. Janos, Ludvik, A linerization of Semiflows in the Hilbert Space l. Topology proceedings, volum. 2 (1970), 219-232. Google Scholar

[6] 6. Janos, Ludvik and Solomon, J. L., A Fixed Point Theorem and Attractors. Proc. Amer. Math. Soc. 71, (2), (1977), 257-262. Google Scholar

[7] 7. Kelley, J. L., General Topology. Van Nostrand, New York, 1955. Google Scholar

[8] 8. McCann, Roger C., Asymptotically Stable Dynamical Systems are Linear, Pacific J. Math. 81 (1979), 475-479. Google Scholar

[9] 9. McCann, Roger C., Embedding Asymptotically Stable Dynamical Systems into Radial Flows in l. Pacific J. Math. 90 (1980) 425-429. Google Scholar

[10] 10. Sine, Robert, Structure and Asymptotic Behavior of Abstract Dynamical Systems. Non-linear Analysis, Theory, Methods and Applications. Vol. 2, No. 1 (1978), 119-127. Google Scholar

[11] 11. de Vries, J., A Note on Topological Linearization of Locally Compact Transformation Groups in Hilbert Space. Math. System Theory, Vol. 6, No. 1, 49-59. Google Scholar

Cité par Sources :