On the existence of chaotic behaviour of diffeomorphisms

Michal Fečkan

Applications of Mathematics (1993)

  • Volume: 38, Issue: 2, page 101-122
  • ISSN: 0862-7940

Abstract

top
For several specific mappings we show their chaotic behaviour by detecting the existence of their transversal homoclinic points. Our approach has an analytical feature based on the method of Lyapunov-Schmidt.

How to cite

top

Fečkan, Michal. "On the existence of chaotic behaviour of diffeomorphisms." Applications of Mathematics 38.2 (1993): 101-122. <http://eudml.org/doc/15739>.

@article{Fečkan1993,
abstract = {For several specific mappings we show their chaotic behaviour by detecting the existence of their transversal homoclinic points. Our approach has an analytical feature based on the method of Lyapunov-Schmidt.},
author = {Fečkan, Michal},
journal = {Applications of Mathematics},
keywords = {bifurcations; homoclinic orbits; chaotic behaviour; chaos; bifurcation; diffeomorphisms; homoclinic orbits},
language = {eng},
number = {2},
pages = {101-122},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the existence of chaotic behaviour of diffeomorphisms},
url = {http://eudml.org/doc/15739},
volume = {38},
year = {1993},
}

TY - JOUR
AU - Fečkan, Michal
TI - On the existence of chaotic behaviour of diffeomorphisms
JO - Applications of Mathematics
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 38
IS - 2
SP - 101
EP - 122
AB - For several specific mappings we show their chaotic behaviour by detecting the existence of their transversal homoclinic points. Our approach has an analytical feature based on the method of Lyapunov-Schmidt.
LA - eng
KW - bifurcations; homoclinic orbits; chaotic behaviour; chaos; bifurcation; diffeomorphisms; homoclinic orbits
UR - http://eudml.org/doc/15739
ER -

References

top
  1. K. R. Meyer & C. R. Sell, Melnikov transforms, Bernoulli bundles, and almost periodic perturbations, Trans. Amer. Math. Soc. 314 (1) (1989), 63-105. (1989) MR0954601
  2. K. J. Palmer, 10.1007/978-3-322-96656-8_5, Dynamics Reported 1 (1988), 265-306. (1988) Zbl0676.58025MR0945967DOI10.1007/978-3-322-96656-8_5
  3. K. J. Palmer, 10.1016/0022-0396(84)90082-2, J. Diff. Equations 55 (1984), 225-256. (1984) Zbl0508.58035MR0764125DOI10.1016/0022-0396(84)90082-2
  4. S. N. Chow, J . K. Hale & J. Mallet-Paret, 10.1016/0022-0396(80)90104-7, J. Diff. Equations 37 (1980), 351-373. (1980) MR0589997DOI10.1016/0022-0396(80)90104-7
  5. M. Fečkan, Bifurcations of heteroclinic orbits for diffeomorfisms, Aplikace Matematiky 36 (1991), 355-367. (1991) MR1125637
  6. S. Smale, Diffeomorphisms with infinitely many periodic points, in Differential and Combinatorical Topology, Princeton Univ. Press, New Jersey, 1963, pp. 63-80. (1963) MR0182020
  7. C. Pugh M. Shub & M. W. Hirsch, Invariant Manifolds, Lec. Not. Math. 583, Springer- -Verlag, New York, 1977. (1977) MR0501173
  8. S. Wiggins, 10.1007/978-1-4612-1042-9, Appl. Math. Sci. 73, Springer- Verlag, New York, 1988. (1988) Zbl0661.58001MR0956468DOI10.1007/978-1-4612-1042-9
  9. D. Henry, 10.1007/BFb0089647, Lec. Not. Math. 840, Springer- Verlag, New York, 1981. (1981) Zbl0456.35001MR0610244DOI10.1007/BFb0089647
  10. M. W. Hirsh & S. Smale, Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press, New York, 1974. (1974) MR0486784
  11. M. L. Glasser V. G. Papageoriou & T. C. Bountis, 10.1137/0149040, SIAM J. Appl. Math. 49 (1989), 692-703. (1989) MR0997915DOI10.1137/0149040
  12. M. Medveď, Dynamical Systems, Veda, Bratislava, 1988. (In Slovak.) (1988) MR0982929

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.