A Characterization of ω -Limit Sets for Continuous Flows on Surfaces

Víctor Jiménez López; Gabriel Soler López

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 2, page 515-521
  • ISSN: 0392-4033

Abstract

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An explicit topological description of ω-limit sets of continuous flows on compact surfaces without boundary is given. Some of the results can be extended to manifolds of larger dimensions.

How to cite

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Jiménez López, Víctor, and Soler López, Gabriel. "A Characterization of $\omega$-Limit Sets for Continuous Flows on Surfaces." Bollettino dell'Unione Matematica Italiana 9-B.2 (2006): 515-521. <http://eudml.org/doc/289599>.

@article{JiménezLópez2006,
abstract = {An explicit topological description of ω-limit sets of continuous flows on compact surfaces without boundary is given. Some of the results can be extended to manifolds of larger dimensions.},
author = {Jiménez López, Víctor, Soler López, Gabriel},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {515-521},
publisher = {Unione Matematica Italiana},
title = {A Characterization of $\omega$-Limit Sets for Continuous Flows on Surfaces},
url = {http://eudml.org/doc/289599},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Jiménez López, Víctor
AU - Soler López, Gabriel
TI - A Characterization of $\omega$-Limit Sets for Continuous Flows on Surfaces
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/6//
PB - Unione Matematica Italiana
VL - 9-B
IS - 2
SP - 515
EP - 521
AB - An explicit topological description of ω-limit sets of continuous flows on compact surfaces without boundary is given. Some of the results can be extended to manifolds of larger dimensions.
LA - eng
UR - http://eudml.org/doc/289599
ER -

References

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  1. ANOSOV, D. V., Flows on closed surfaces and behavior of trajectories lifted to the universal covering plane, J. Dynam. Control Systems, 1 (1995), 125-138. Zbl0995.37014
  2. BALIBREA, F. - JIMÉNEZ LÓPEZ, V., A characterization of the ω-limit sets of planar continuous dynamical sistems, J. Differential Equations, 145 (1996), 469-488. 
  3. JIMÉNEZ LÓPEZ, V. - SOLER LÓPEZ, G., A topological characterization of ω-limit sets for continuous flows on the projective plane, Discrete Contin. Dynam. Systems, Added Volume (2001), 254-258. Zbl1301.37028
  4. JIMÉNEZ LÓPEZ, V. - SOLER LÓPEZ, G., A characterization of ω-limit sets of nonrecurrent orbits in 𝕊 n , Internat. J. Bifur. Chaos Appl. Sci. Engrg., 13 (2003), 1727-1732. Zbl1056.37007
  5. JIMÉNEZ LÓPEZ, V. - SOLER LÓPEZ, G., Accumulation points of nonrecurrent orbits of surface flows, Topology Appl., 137 (2004), 187-194. 
  6. JIMÉNEZ LÓPEZ, V. - SOLER LÓPEZ, G., Transitive flows on manifolds, Rev. Mat. Iberoamericana, 20 (2004), 107-130. 
  7. SMITH, R. A. - THOMAS, S., Some examples of transitive smooth flows on differentiable manifolds, J. London Math. Soc., 37 (1988), 552-568. Zbl0634.58025
  8. SMITH, R. A. - THOMAS, S., Transitive flows on two-dimensional manifolds, J. London Math. Soc., 37 (1988), 569-576. Zbl0634.58026
  9. SOLER LÓPEZ, G., Accumulation points of flows on the Klein bottle, Discrete Contin. Dynam. Systems, 9 (2003), 497-503. 
  10. SOLER LÓPEZ, G., ω-limit sets from nonrecurrent points of flows on manifold, Topology Appl., 153 (2005), 963-974. Zbl1085.37013
  11. SOLER LÓPEZ, G., Caracterización topólogica de conjuntos ω-límite sobre variedades, PhD. Thesis, Universidad de Murcia, 2005. 
  12. VINOGRAD, R. E., On the limiting behavior of an unbounded integral curve, Moskov. Gos. Univ. Uč. Zap., 155, Mat. 5 (1952), 94-136 (in Russian). 

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