# Thirty years after Sharkovskii's Theorem: new perspectives

- Dates:
- 13.06.94 - 18.06.94
- Place:
- La Manga del Mar Menor, Spain
- Organizers:
- Lluís Alsedà, Francisco Balibrea (Universidad de Murcia), Jaume Llibre and Michal Misiurewicz (Indiana University - PurdueUniversity)

#### Proceedings

The Proceedings of the Simposium have been published in International Bifurcation and Chaos in applied sciences and engineering Vol. 5 Num. 5 1995 (World Scientific) and reprinted in World Scientific Series on Nonlinear Science. Series B: Special Theme Issues and Proceedings, 8. World Scientific Publishing Co., Inc., River Edge, NJ, 1995. ISBN: 981-02-2504-0 58-06 (both issues include the Juan Tolosa's translation to the english language of the seminal paper "Coexistence of cycles of a continuous map of the line into itself" by A. N. Sharkovskii)

#### Participants

A. Al-Dhahir, Ll. Alsedà, S. Baldwin, F. Balibrea, M.M. Barge, C. Bernhardt, L. Block, A. Blokh, J. Bobok, I. Bosch, K.M. Brucks, H. Bruin, S. Buckley, A. Cabrera, J. Cánovas, M. Chas, E.M. Coven, K. Dale, M. del Rio, B. Diamond, F. Esquembre, A. Falco, V. Fedorenko, L. Feng, W. Geller, C. Grácio, J. Guaschi, V. Jiménez, S. Kolyada, M. Kuchta, C. La Paz, H. Langenberg, C. Leseduarte, A. Linero, J. Llibre, J. Los, M. Misiurewicz, F. Mondejar, G. Mora, J.M. Moreno, P. Mumbru, Z. Nitecki, A. Nunes, F. O'Cairbre, A. O'Reilly, J. Paraños, J. Parra, P. Raith, G. Rodriguez, J.A. Rodriguez, J. Rojo, R. Severino, A.N. Sharkovsky, S. Silberger, J. Smítal, L. Snoha, J. Sousa Ramos, W. Szlenk, A. Tendero, J. Tolosa, J. Wosko.#### Lectures

Ll. Alsedà | "Badly ordered cycles of circle maps" |

S. Baldwin | "Periods for tree-maps" |

F. Balibrea | "A characterization of the nonwandering points that are not w-limit points for continuous maps with zero entropy" |

M. Barge | "Homeomorphisms of inverse limit spaces" |

C. Bernhanrdt | "Self-similarity maps on the set of unimodal cycles" |

L. Block | "On homeomorphisms of (I,f) having zero entropy" |

A. Blokh | "Rotation numbers for one-dimensional maps" |

J. Bobok | "Transitive F-cycles versus register shifts for piecewise monotone maps" |

K. Brucks | "A Farey tree organization of locking regions for simple circle maps" |

H. Bruin | "Unimodal maps as Markov chains" |

E. Coven | "Sharkovskii type of cycles" |

B. Diamond | "Stable and unstable manifold structures in the Hénon Map" |

F. Esquembre | "A differentiable triangular map of class 2 with positive topological entropy"^{oo} |

A. Falcó | "A characterization of the kneading sequences for a class of circle maps" |

V. Fedorenko | "Complex and simple maps of the one dimensional manifolds" |

L. Feng | "Zero entropy circle maps" |

W. Geller | "Patterns of maximal entropy" |

J. Guaschi | "Periods of disk homeomorphisms" |

V. Jiménez | "There are no piecewise linear maps of type 2^{oo}^{"} |

S. Kolyada | "On topological dynamics of sequences of continuous maps" |

M. Kuchta | "X-minimal patterns and generalization of Sharkovskii's theorem" |

J. Llibre | "Periods for maps on the figure-eight space" |

J. Los | "Forcing for surface homeomorphisms. A structure theorem" |

M. Misiurewicz | "Thirty years later" |

J.M. Moreno | "Primary strongly directed orbits of self maps of X" |

P. Mumbrú | "Piecewise monotone models for patterns of tree maps" |

Z. Nitecki | "Forcing among polycyclic permutations" |

A. Nunes | "Lefscehtz numbers for transversal maps" |

P. Raith | "The dynamics of piecewise monotonic maps under small perturbations" |

J.A. Rodríguez | "On the extension of the Sharkovskii's theorem for connected graphs with non-positive Euler characteristic" |

J. Rojo | "Fractality on transfinite dimensional spaces" |

R. Severino | "K-Theory and bimodal maps" |

A.N. Sharkovskii | "Universal phenomena in some boundary value problems" |

J. Smital | "Specification property and the space of probability distributions generated by the pairs of trajectories of a continuous map on the interval" |

L. Snoha | "Topologically transitive low dimensional maps" |

J. Tolosa | "Computing the limit entropy of snakes" |

J. Wosko | "A remark on the operator in L with lower-bound function"^{1} |