Thirty Years after Sharkovskiĭ's Theorem: New Perspectives

These proceedings contain a collection of papers on Combinatorial Dynamics, from the lectures that took place during the international symposium, Thirty Years after Sharkovskiĭ's Theorem: New Perspectives, which was held at La Manga del Mar Menor, Murcia, Spain, from June 13 to June 18, 1994.

Since Professor A N Sharkovskiĭ's landmark paper on the coexistence of periods for interval maps, several lines of research have been developed, opening applications of models to help understand a number of phenomena from a wide variety of fields, such as biology, economics, physics, etc. The meeting served to summarize the progress made since Professor Sharkovskiĭ's discovery, and to explore new directions.

• Coexistence of Cycles of a Continuous Map of the Line into Itself (A N Sharkovskiĭ)
• Thirty Years After Sharkovskiĭ's Theorem (M Misiurewicz)
• Dry Turbulence and Period-Adding Phenomena from a 1-D Map with Time Delay (A N Sharkovsky et al.)
• Open Problems Session (M Chas & S Silberger)
• Toward a Theory of Forcing on Maps of Trees (S Baldwin)
• Self-Similarity Maps for the Set of Unimodal Cycles (C Bernhardt)
• Zero Entropy Permutations (L BLock et al.)
• Combinatorics of the Kneading Map (H Bruin)
• Simple and Complex Dynamics for One-Dimensional Manifold Maps (V Fedorenko)
• Periods for Maps of the Figure-Eight Space (C Gillot & J Llibre)
• Periodic Points of C1 Maps and the Asymptotic Lefschetz Number (J Guaschi & J Llibre)
• Maps with Random Perturbations are Generically Not Chaotic (K Janková & J Smítal)
• Order and Chaos for a Class of Piecewise Linear Maps (V J López)
• and other papers