Skip to main content
SpringerLink
Log in

Parallelizability in Banach spaces: Applications of negligibility theory

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. R. D. Anderson and R. H. Bing, A complete elementary proof that Hilbert-space is homeomorphic to the countable infinite product of lines,Bull. Amer. Math. Soc.,74 (1968), 771–792.

    Google Scholar 

  2. J. Auslander and P. Seibert, Prolongations and stability in dynamical systems,Ann. Inst. Fourier,14 (1964), 237–268.

    Google Scholar 

  3. N. P. Bhatia and G. P. Szegő,Dynamical Systems: Stability Theory and Applications, Springer (Berlin, 1967).

    Google Scholar 

  4. R. H. Bing, The Cartesian product of a certain nonmanifold and a line isE 4,Ann. Math.,70 (1959), 399–412.

    Google Scholar 

  5. W. C. Chewning, A dynamical system onE 4 neither isomorphic nor equivalent to a differential system,Bull. Amer. Math. Soc. 80 (1974), 150–153.

    Google Scholar 

  6. W. C. Chewning and R. S. Owen, Local sections of flows on manifolds,Proc. Amer. Math. Soc.,49 (1975), 71–77.

    Google Scholar 

  7. C. Coleman, Hyperbolic stationary points, inReports of the Fifth International Congress on Nonlinear Oscillations, Vol. 2, 222–226, Izd. Inst. Mat. Akad. Nauk Ukrainen SSR (Kiev, 1970).

    Google Scholar 

  8. W. H. Cutler, Negligible subsets for infinite-dimensional Fréchet manifolds,Proc. Amer. Math. Soc.,23 (1969), 668–675.

    Google Scholar 

  9. J. Egawa, A remark on the flow near a compact invariant set,Proc. Japan Acad.,49 (1973), 247–251.

    Google Scholar 

  10. R. Engelking,General Topology, PWN (Warsaw, 1977).

    Google Scholar 

  11. B. M. Garay, Metrization and Liapunov functions. IV,Coll Math. Soc. J. Bolyai 47. Diff. Eqi.: Qualitative theory (Szeged, 1984).

  12. B. M. Garay and J. J. Schäffer, More on uniqueness without continuous dependence in infinite dimensions,J. Diff. Eq. (in print).

  13. S. K. Goel and D. A. Neumann, Completely unstable dynamical systems,Trans. Amer. Math. Soc.,291 (1985), 639–668.

    Google Scholar 

  14. O. Hajek, Parallelizability revisited,Proc. Amer. Math. Soc. 27 (1971), 77–84.

    Google Scholar 

  15. J. P. Henderson and J. J. Walsh, Examples of cell-like decompositions of the infinite-dimensional manifolds σ and Σ,Topology Appl.,16 (1983), 143–155.

    Google Scholar 

  16. K. W. Kwun, Factors ofN-space,Mich. Math. J.,9 (1962), 207–211.

    Google Scholar 

  17. E. Luft, On contractible open topological manifolds,Invent. Math.,4 (1967), 192–201.

    Google Scholar 

  18. L. Márkus, Parallel dynamical systems,Topology,8 (1969), 47–57.

    Google Scholar 

  19. R. C. McCann, Continuous flows with Hausdorff orbit spaces,Funkcial. Ekvac.,18 (1975), 195–206.

    Google Scholar 

  20. R. C. McCann, On the parallelizability of regions of asymptotic stability,Funkcial. Ekvac.,23 (1980), 357–360.

    Google Scholar 

  21. D. A. Neumann, Smoothing continuous flows,J. Diff. Eq.,24 (1977), 127–135.

    Google Scholar 

  22. D. A. Neumann, Topologically hyperbolic equilibria in dynamical systems,J. Diff. Eq.,37 (1980), 49–59.

    Google Scholar 

  23. J. Palis, On the local structure of hyperbolic points in Banach spaces,An. Acad. Brasil. Ci.,40 (1968), 263–266.

    Google Scholar 

  24. D. Pixton, More counterexamples to Coleman's conjecture,Proc. Amer. Math. Soc.,82 (1981), 145–148.

    Google Scholar 

  25. T. Saito, On the structure of compact dynamical systems,Funkcional. Ekvac.,13 (1970), 147–170.

    Google Scholar 

  26. T. Ura and J. Egawa, Isomorphism and parallelizability in dynamical systems theory.Math. Systems Theory,7 (1973), 250–264.

    Google Scholar 

  27. T. Ura and I. Kimura, Sur le courant exterieur a une region invariante. Theoreme de Bendixson,Comm. Math. Univ. Sanctii Pauli. 8 (1960), 23–39.

    Google Scholar 

  28. R. B. Walker, Topological versus differentiable hyperbolicity: extending orbit conjugacies,J. Diff. Eq.,43 (1982), 451–473.

    Google Scholar 

  29. J. E. West, The diffeomorphic excision of closed local compacta from infinite-dimensional Hilbert manifolds,Comp. Math.,21 (1969), 271–291.

    Google Scholar 

  30. J. H. C. Whitehead, A certain open manifold whose groups is unity,Q. J. Math. 6 (1935), 268–279.

    Google Scholar 

  31. F. W. Wilson, The structure of the level surfaces of a Liapunov function,J. Diff. Eq.,3 (1967), 323–329.

    Google Scholar 

  32. F. W. Wilson, A reformulation of Coleman's conjecture concerning the local conjugacy of topologically hyperbolic singular points, inStructure of Attractors in Dynamical Systems, Springer (Berlin, 1978).

    Google Scholar 

  33. F. W. Wilson, A uniform continuity condition which is equivalent to Coleman's conjecture,J. Diff. Eq.,36 (1980), 12–19.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Budapest University of Technology, H-1521, Budapest

    B. M. Garay

Authors
  1. B. M. Garay
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Garay, B.M. Parallelizability in Banach spaces: Applications of negligibility theory. Acta Math Hung 53, 3–22 (1989). https://doi.org/10.1007/BF02170050

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02170050

Search

Navigation