Combinatorial Patterns For Maps Of The Interval

Buch | Softcover

1991
American Mathematical Society (Verlag)
9780821825136 (ISBN)

Infos

In recent years, motivated by Shrkovskii's theorem, researchers have realized that a good deal of information about the dynamics of a map on the interval can be deduced from the combinatorial structure of its periodic orbits. This data can be formulated as a 'forcing' relation between cyclic permutations (representing 'orbit types' of periodic orbits). The present study investigates a number of new features of this relation and its generalization to multicyclic permutations (modelling finite unions of periodic orbits) and combinatorial patterns (modelling finite invariant sets). A central theme is the role of reductions and extensions of permutations. Results include: (i) a 'combinatorial shadowing theorem' and its application to approximating permutations by cycles in the forcing relation; (ii) the distribution of different representatives of a given cycle in one (adjusted) map; (iii) characterization of the forcing-maximal permutations and patterns of fixed degree; and (iv) a calculation of the asymptotic growth rate of the maximum entropy forced by a permutation of given degree.

Produkt-Details

• Erscheint lt. Verlag: 30.7.1991
• Reihe/Serie: Memoirs of the American Mathematical Society
• Verlagsort: Providence
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Schlagworte: Memoirs of the AMS; No. 456
• ISBN-13: 9780821825136 / 9780821825136
• Zustand: Neuware