A+ CATEGORY SCIENTIFIC UNIT

Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval

Volume 160 / 1999

Sergiĭ Kolyada, Michał Misiurewicz, L’ubomír Snoha Fundamenta Mathematicae 160 (1999), 161-181 DOI: 10.4064/fm-160-2-161-181

Abstract

The topological entropy of a nonautonomous dynamical system given by a sequence of compact metric spaces $(X_i)^∞_{i = 1}$ and a sequence of continuous maps $(f_i)^∞_{i = 1}$, $f_i : X_i → X_{i+1}$, is defined. If all the spaces are compact real intervals and all the maps are piecewise monotone then, under some additional assumptions, a formula for the entropy of the system is obtained in terms of the number of pieces of monotonicity of $f_n ○... ○ f_2 ○ f_1$. As an application we construct a large class of smooth triangular maps of the square of type $2^∞$ and positive topological entropy.

Authors

  • Sergiĭ Kolyada
  • Michał Misiurewicz
  • L’ubomír Snoha

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image