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Conference Proceedings
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6th EUROMECH Nonlinear Dynamics Conference (ENOC 2008)
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Topological semi-conjugacy and chaotic mappings
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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.