# Each nowhere dense nonvoid closed set in Rn is a σ-limit set

Fundamenta Mathematicae (1996)

- Volume: 149, Issue: 2, page 183-190
- ISSN: 0016-2736

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topSivak, Andrei. "Each nowhere dense nonvoid closed set in Rn is a σ-limit set." Fundamenta Mathematicae 149.2 (1996): 183-190. <http://eudml.org/doc/212116>.

@article{Sivak1996,

abstract = {We discuss main properties of the dynamics on minimal attraction centers (σ-limit sets) of single trajectories for continuous maps of a compact metric space into itself. We prove that each nowhere dense nonvoid closed set in $ℝ^n$, n ≥ 1, is a σ-limit set for some continuous map.},

author = {Sivak, Andrei},

journal = {Fundamenta Mathematicae},

keywords = {dynamical systems; iterations; continuous maps},

language = {eng},

number = {2},

pages = {183-190},

title = {Each nowhere dense nonvoid closed set in Rn is a σ-limit set},

url = {http://eudml.org/doc/212116},

volume = {149},

year = {1996},

}

TY - JOUR

AU - Sivak, Andrei

TI - Each nowhere dense nonvoid closed set in Rn is a σ-limit set

JO - Fundamenta Mathematicae

PY - 1996

VL - 149

IS - 2

SP - 183

EP - 190

AB - We discuss main properties of the dynamics on minimal attraction centers (σ-limit sets) of single trajectories for continuous maps of a compact metric space into itself. We prove that each nowhere dense nonvoid closed set in $ℝ^n$, n ≥ 1, is a σ-limit set for some continuous map.

LA - eng

KW - dynamical systems; iterations; continuous maps

UR - http://eudml.org/doc/212116

ER -

## References

top- [1] S. Agronsky, A. Bruckner, J. Ceder and T. Pearson, The structure of ω-limit sets for continuous functions, Real Anal. Exchange 15 (1989-90), 483-510. Zbl0728.26006
- [2] A. Bruckner and J. Smítal, The structure of ω-limit sets for continuous maps of the interval, Math. Bohem. 117 (1992), 42-47. Zbl0762.26003
- [3] H. Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton Univ. Press, Princeton, N.J., 1981. Zbl0459.28023
- [4] H. Hilmy, Sur les centres d'attraction minimaux dans les systèmes dynamiques, Compositio Math. 3 (1936), 227-238. Zbl62.0992.11
- [5] N. Kryloff et N. Bogoliouboff [N. Krylov et N. Bogolyubov], La théorie générale de la mesure dans son application à l'étude des systèmes de la mécanique non linéaire, Ann. of Math. (2) 38 (1937), 65-113. Zbl0016.08604
- [6] V. V. Nemytskiĭ and V. V. Stepanov, Qualitative Theory of Differential Equations, Princeton Univ. Press, Princeton, N.J., 1960. Zbl0089.29502
- [7] A. N. Sharkovskiĭ, Attracting and attracted sets, Dokl. Akad. Nauk SSSR 160 (1965), 1036-1038 (in Russian); English transl.: Soviet Math. Dokl. 6 (1965), 268-270.
- [8] A. G. Sivak, The structure of minimal attraction centers of trajectories of continuous maps of the interval, Real Anal. Exchange 20 (1994/95), 125-133. Zbl0824.54021

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