Title: Approximation of entropy on hyperbolic sets for one-dimensional maps and their multidimensional perturbations
Authors: Li, Ming-Chia
Malkin, M. I.
Department of Applied Mathematics
Keywords: chaotic dynamics;difference equations;one-dimensional maps;topological entropy;hyperbolic orbits
Issue Date: 1-Jun-2010
Abstract: We consider piecewise monotone (not necessarily, strictly) piecewise C (2) maps on the interval with positive topological entropy. For such a map f we prove that its topological entropy h (top)(f) can be approximated (with any required accuracy) by restriction on a compact strictly f-invariant hyperbolic set disjoint from some neighborhood of prescribed set consisting of periodic attractors, nonhyperbolic intervals and endpoints of monotonicity intervals. By using this result we are able to generalize main theorem from [1] on chaotic behavior of multidimensional perturbations of solutions for difference equations which depend on two variables at nonperturbed value of parameter.
URI: http://dx.doi.org/10.1134/S1560354710020097
ISSN: 1560-3547
DOI: 10.1134/S1560354710020097
Volume: 15
Issue: 2-3
Begin Page: 210
End Page: 221
Appears in Collections:Articles

Files in This Item:

  1. 000277098300009.pdf