Conjugacy of normally tangent diffeomorphisms : a tool for treating moduli of stability

Patrick Bonckaert

Annales de l'institut Fourier (1990)

  • Volume: 40, Issue: 1, page 213-236
  • ISSN: 0373-0956

Abstract

top
We give sufficient conditions for the conjugacy of two diffeomorphisms coinciding on a common invariant submanifold V and with equal normal derivative; moreover we obtain that the homeomorphism h realizing this conjugacy satisfies additional inequalities. These inequalities, implying also the existence of the normal derivative of h along V, serve to extend this conjugacy towards regions where moduli of stability are present.

How to cite

top

Bonckaert, Patrick. "Conjugacy of normally tangent diffeomorphisms : a tool for treating moduli of stability." Annales de l'institut Fourier 40.1 (1990): 213-236. <http://eudml.org/doc/74872>.

@article{Bonckaert1990,
abstract = {We give sufficient conditions for the conjugacy of two diffeomorphisms coinciding on a common invariant submanifold V and with equal normal derivative; moreover we obtain that the homeomorphism h realizing this conjugacy satisfies additional inequalities. These inequalities, implying also the existence of the normal derivative of h along V, serve to extend this conjugacy towards regions where moduli of stability are present.},
author = {Bonckaert, Patrick},
journal = {Annales de l'institut Fourier},
keywords = {conjugacy; diffeomorphisms; moduli of stability},
language = {eng},
number = {1},
pages = {213-236},
publisher = {Association des Annales de l'Institut Fourier},
title = {Conjugacy of normally tangent diffeomorphisms : a tool for treating moduli of stability},
url = {http://eudml.org/doc/74872},
volume = {40},
year = {1990},
}

TY - JOUR
AU - Bonckaert, Patrick
TI - Conjugacy of normally tangent diffeomorphisms : a tool for treating moduli of stability
JO - Annales de l'institut Fourier
PY - 1990
PB - Association des Annales de l'Institut Fourier
VL - 40
IS - 1
SP - 213
EP - 236
AB - We give sufficient conditions for the conjugacy of two diffeomorphisms coinciding on a common invariant submanifold V and with equal normal derivative; moreover we obtain that the homeomorphism h realizing this conjugacy satisfies additional inequalities. These inequalities, implying also the existence of the normal derivative of h along V, serve to extend this conjugacy towards regions where moduli of stability are present.
LA - eng
KW - conjugacy; diffeomorphisms; moduli of stability
UR - http://eudml.org/doc/74872
ER -

References

top
  1. [1] M. BERGER, P. GAUDUCHON and E. MAZET, Le Spectre d'une Variété Riemannienne, Lecture Notes in Mathematics 194, Springer-Verlag, Berlin-Heidelberg-New York (1971). Zbl0223.53034MR43 #8025
  2. [2] P. BONCKAERT, F. DUMORTIER and S. STRIEN, Singularities of Vector fields on R3 determined by their first nonvanishing jet, Ergodic Theory and Dynamical Systems, 9 (1989) 281-308. Zbl0661.58005
  3. [3] H. BRAUNER, Differentialgeometrie, Viewig, Braunschweig, 1981. Zbl0466.53001MR82h:53001
  4. [4] M.W. HIRSCH, Differential Topology, Springer, New York, 1976. Zbl0356.57001MR56 #6669
  5. [5] M.W. HIRSCH, C. PUGH and M. SHUB, Invariant Manifolds, Lecture Notes in Math., 583, Springer-Verlag, Berlin-Heidelberg-New York, 1977. Zbl0355.58009MR58 #18595
  6. [6] J.L. KELLEY, General Topology, Van Nostrand, New York, 1955. Zbl0066.16604MR16,1136c
  7. [7] R. LABARCA and M.J. PACIFICO, Morse-Smale vector fields on 4-manifolds with boundary, Dynamical Systems and bifurcation theory, Pitman series 160, Longman, 1987. Zbl0632.58023MR89e:58066
  8. [8] S. LANG, Differential Manifolds, Addison-Wesley, Reading Massachusetts, 1972. Zbl0239.58001MR55 #4241
  9. [9] W. de MELO, Moduli of Stability of two-dimensional diffeomorphisms, Topology 19 (1980), 9-21. Zbl0447.58025MR81c:58047
  10. [10] W. de MELO and F. DUMORTIER, A type of moduli for saddle connections of planar diffeomorphisms, J. of Diff. Eq. 75 (1988), 88-102. Zbl0672.58036MR90a:58137
  11. [11] J. PALIS, A differentiable invariant of topological conjugacies and moduli of stability, Astérisque, 51 (1978), 335-346. Zbl0396.58015MR58 #13189
  12. [12] M. SPIVAK, Differential Geometry, Volume I, Publish or Peris Inc., Berkeley, 1979. 
  13. [13] S. van STRIEN, Normal hyperbolicity and linearisability, Invent. Math., 87 (1987), 377-384. Zbl0619.58033MR88f:58088
  14. [14] S. van STRIEN, Linearisation along invariant manifolds and determination of degenerate singularies of vector fields in R3, Delft Progr. Rep., 12 (1988), 107-124. Zbl0825.58029MR90d:58117
  15. [15] S. van STRIEN, Smooth linearization of hyperbolic fixed points without resonace conditions, preprint. Zbl0726.58039
  16. [16] S. van STRIEN and G. TAVARES DA SANTOS, Moduli of stability for germs of homogeneous vector fields on R3, J. of Diff. Eq., 69 (1987), 63-84. Zbl0633.58031

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.