# IPACS Electronic library

## Topological semi-conjugacy and chaotic mappings

Inese Bula
We analyze $\alpha_m$-mappings ($m>=2$) in symbol space $\Sigma_2$ and prove that the maps are chaotic in $\Sigma_2$. We show that there exists semi-conjugacy between $\alpha_m: I\to I$ ($I\subset \Sigma_2$) and corresponding class $E_m$ of mappings in $[0,1[$. The topological semi-conjugacy and sensitive dependence on initial conditions guarantee that mappings $E_m$ are chaotic.