Navegar

Colección

Datos Estadísticas

Artículo

Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

We present a method for estimating the minimal periodic orbit structure, the topological entropy, and a fat representative of the homeomorphism associated with the existence of a finite collection of periodic orbits of an orientation-preserving homeomorphism of the disk D 2. The method focuses on the concept of fold and recurrent bogus transition and is more direct than existing techniques. In particular, we introduce the notion of complexity to monitor the modification process used to obtain the desired goals. An algorithm implementing the procedure is described and some examples are presented at the end. © 2005 Springer.

Registro:

Documento: Artículo
Título:Minimal periodic orbit structure of 2-dimensional homeomorphisms
Autor:Solari, H.G.; Natiello, M.A.
Filiación:Dept. de FIsica, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires, Argentina
Centre for Mathematical Sciences, Lund University, Box 118, S-221 00 Lund, Sweden
Palabras clave:Anosov representative; D homeomorphisms of the disk; Thurston classification theorem
Año:2005
Volumen:15
Número:3
Página de inicio:183
Página de fin:222
DOI: http://dx.doi.org/10.1007/s00332-005-0637-1
Título revista:Journal of Nonlinear Science
Título revista abreviado:J. Nonlinear Sci.
ISSN:09388974
CODEN:JNSCE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09388974_v15_n3_p183_Solari

Referencias:

  • Holmes, P., Williams, R.F., Knotted periodic orbits in suspensions of Smale's horseshoe: Torus knots and bifurcation sequences (1985) Arch. Rat. Mech. Anal., 90, p. 115
  • Boyland, P., (1984) Braid Types and A Topological Method of Proving Positive Topological Entropy, , Preprint, Department of Mathematics, Boston University
  • Natiello, M.A., Solari, H.G., Remarks on braid theory and the characterisation of periodic orbits (1994) J. Knot Theory Ramifications, 3, p. 511
  • Solari, H.G., Natiello, M.A., Vazquez., M., Braids on the poincaŕe section: A laser example (1996) Phys. Rev., E54, p. 3185
  • Hall, T., Fat one-dimensional representatives of pseudo-Anosov isotopy classes with minimal periodic orbit structure (1994) Nonlinearity, 7, pp. 367-384
  • Thurston, W.P., On the geometry and dynamics of diffeomorphisms of surfaces (1988) Bull. Am. Math. Soc., 19, p. 417
  • Gambaudo, J.M., Van Strien, S., Tresser, C., The periodic orbit structure of orientationpreserving diffeomorphisms on D2 with topological entropy zero (1989) Ann. Inst. Henri Poincaŕe Phys. th'Eor., 49, p. 335
  • Casson, A., Bleiler, S., (1988) Automorphisms of Surfaces after Nielsen and Thurston, , Cambridge University Press Cambridge
  • Bestvina, M., Handel, M., Train tracks and automorphisms of free groups (1992) Ann. Math., 135, pp. 1-51
  • Bestvina, M., Handel, M., Train tracks for surface homeomorphisms (1995) Topology, 34, pp. 109-140
  • Los, J.E., Pseudo-Anosov maps and invariant train tracks in disks: A finite algorithm (1993) Proc. London Math. Soc., 66, pp. 400-430
  • Franks, J., Misiurewicz, M., Cycles for disk homeomorphisms and thick trees (1993) Contemp. Math., 152, pp. 69-139
  • Gilmore, R., Topological analysis of chaotic dynamical systems (1999) R. Mod. Phys., 70, pp. 1455-1530
  • Hayakawa, E., Markov maps on trees (2000) Math. Japonica, 31, pp. 235-240
  • De Carvallo, A., Hall, T., Pruning theory and Thurston's classification of surface homeomorphisms (2001) J. Eur. Math. Soc., 3, pp. 287-333

Citas:

---------- APA ----------
Solari, H.G. & Natiello, M.A. (2005) . Minimal periodic orbit structure of 2-dimensional homeomorphisms. Journal of Nonlinear Science, 15(3), 183-222.
http://dx.doi.org/10.1007/s00332-005-0637-1
---------- CHICAGO ----------
Solari, H.G., Natiello, M.A. "Minimal periodic orbit structure of 2-dimensional homeomorphisms" . Journal of Nonlinear Science 15, no. 3 (2005) : 183-222.
http://dx.doi.org/10.1007/s00332-005-0637-1
---------- MLA ----------
Solari, H.G., Natiello, M.A. "Minimal periodic orbit structure of 2-dimensional homeomorphisms" . Journal of Nonlinear Science, vol. 15, no. 3, 2005, pp. 183-222.
http://dx.doi.org/10.1007/s00332-005-0637-1
---------- VANCOUVER ----------
Solari, H.G., Natiello, M.A. Minimal periodic orbit structure of 2-dimensional homeomorphisms. J. Nonlinear Sci. 2005;15(3):183-222.
http://dx.doi.org/10.1007/s00332-005-0637-1