# Forcing among patterns with no block structure

### Abstract

• Define the following order among all natural numbers except for 2 and 1: \[ 4\gg 6\gg 3\gg \dots \gg 4n\gg 4n+2\gg 2n+1\gg 4n+4\gg\dots \] Let \$f\$ be a continuous interval map. We show that if \$m\gg s\$ and \$f\$ has a cycle with no division (no block structure) of period \$m\$ then \$f\$ has also a cycle with no division (no block structure) of period \$s\$. We describe possible sets of periods of cycles of \$f\$ with no division and no block structure.

### Keywords

• math.DS, math.DS, Primary 37E15, secondary 37E05, 37E45
• ### Author List

• Blokh A; Misiurewicz M