## Dense chaos for continuous interval maps

*Nonlinearity*,
**18**, 1691-1698, 2005.

### Abstract

A continuous map *f* from a compact interval *I* into itself is
densely chaotic if the set of points *(x,y)* such that
and
is dense in *I*^{ 2}.
We show that if *f* is a densely chaotic interval map then
*f*^{ 2} has
a horseshoe, which implies that its topological entropy is at least
log 2/2 and *f* is of type at most 6 for Sharkovskii's order
(that is, there exists a periodic point of period 6).

Paper:
[arXiv:1901.01064]
[pdf (published paper)]