# Periodic segments and Nielsen numbers

Banach Center Publications (1999)

- Volume: 47, Issue: 1, page 247-252
- ISSN: 0137-6934

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topWójcik, Klaudiusz. "Periodic segments and Nielsen numbers." Banach Center Publications 47.1 (1999): 247-252. <http://eudml.org/doc/208938>.

@article{Wójcik1999,

abstract = {We prove that the Poincaré map $φ_\{(0,T)\}$ has at least $N(\tilde\{h\}, cl(W_\{0\} \ W_\{0\}^\{-\}) )$ fixed points (whose trajectories are contained inside the segment W) where the homeomorphism $\tilde\{h\}$ is given by the segment W.},

author = {Wójcik, Klaudiusz},

journal = {Banach Center Publications},

keywords = {local process; periodic orbit; Poincaré mapping; Nielsen number; exit set},

language = {eng},

number = {1},

pages = {247-252},

title = {Periodic segments and Nielsen numbers},

url = {http://eudml.org/doc/208938},

volume = {47},

year = {1999},

}

TY - JOUR

AU - Wójcik, Klaudiusz

TI - Periodic segments and Nielsen numbers

JO - Banach Center Publications

PY - 1999

VL - 47

IS - 1

SP - 247

EP - 252

AB - We prove that the Poincaré map $φ_{(0,T)}$ has at least $N(\tilde{h}, cl(W_{0} \ W_{0}^{-}) )$ fixed points (whose trajectories are contained inside the segment W) where the homeomorphism $\tilde{h}$ is given by the segment W.

LA - eng

KW - local process; periodic orbit; Poincaré mapping; Nielsen number; exit set

UR - http://eudml.org/doc/208938

ER -

## References

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- [11] R. Srzednicki and K. Wójcik, A Geometric Method for Detecting Chaotic Dynamics, J. Diff. Equat. Vol. 135, (1997), 66-82. Zbl0873.58049
- [12] R. Srzednicki, A Geometric Method for the Periodic Problem in Ordinary Differential Equations, Seminaire D'Analyse Moderne No.22, Eds.: G. Fournier, T. Kaczynski, Université de Sherbrooke 1992. Zbl0822.34039
- [13] K. Wójcik, Isolating segments and symbolic dynamics, to appear in Nonlinear Anal. Th. Meth. Appl. Zbl0955.37005
- [14] X. Z. Zhao, A relative Nielsen number for the complement, Lecture Notes in Math. vol. 1411, Springer-Verlag, 1989, 189-199.

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