## Combinatorial patterns for maps of the interval.(English)Zbl 0745.58019

Mem. Am. Math. Soc. 456, 112 p. (1991).
Let $$f$$ be a continuous map of a closed interval $$I$$ to itself. The authors define a combinatorial pattern $$\theta$$ of $$f$$. They say that a combinatorial pattern $$\theta$$ forces another combinatorial pattern $$\eta$$ if every continuous map $$f: I\to I$$ which exhibits $$\theta$$ also exhibits $$\eta$$.
Some criteria are given for deciding if $$\theta$$ forces $$\eta$$ in any specific case. Extensions and reductions of patterns are studied. The authors investigate a weakening of the notion of extension, which they call combinatorial shadowing. The relation between entropy estimates arising from different patterns is explored.

### MSC:

 37B40 Topological entropy 37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics 54H20 Topological dynamics (MSC2010) 26A18 Iteration of real functions in one variable

### Keywords:

interval map; combinatorial pattern
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