TY - JOUR
T1 - Strict inequalities for the entropy of transitive piecewise monotone maps
AU - Misiurewicz, Michal
AU - Raith, Peter
N1 - Affiliations: Department of Mathematical Sciences, IUPUI, 402 N. Blackford Street, Indianapolis, IN 46202-3216; Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, A 1090 Wien, Austria
Adressen: Misiurewicz, M.; Department of Mathematical Sciences; IUPUI; 402 N. Blackford Street Indianapolis, IN 46202-3216, United States; email: [email protected]
Source-File: 506Scopus.csv
Import aus Scopus: 2-s2.0-23844468231
Importdatum: 24.01.2007 11:22:35
22.10.2007: Datenanforderung 1920 (Import Sachbearbeiter)
04.01.2008: Datenanforderung 2054 (Import Sachbearbeiter)
PY - 2005
Y1 - 2005
N2 - Let T : [0, 1] ? [0, 1] be a piecewise differentiable piecewise monotone map, and let r > 1. It is well known that if |T'| = r (respectively |T'| = r) then htop(T) = log r (respectively htop(T) = log r). We show that if additionally |T'| r) on some subinterval and T is topologically transitive then the inequalities for the entropy are strict. We also give examples that the assumption of piecewise monotonicity is essential, even if T is continuous. In one class of examples the dynamical dimension of the whole interval can be made arbitrarily small.
AB - Let T : [0, 1] ? [0, 1] be a piecewise differentiable piecewise monotone map, and let r > 1. It is well known that if |T'| = r (respectively |T'| = r) then htop(T) = log r (respectively htop(T) = log r). We show that if additionally |T'| r) on some subinterval and T is topologically transitive then the inequalities for the entropy are strict. We also give examples that the assumption of piecewise monotonicity is essential, even if T is continuous. In one class of examples the dynamical dimension of the whole interval can be made arbitrarily small.
M3 - Article
SN - 1078-0947
VL - 13
SP - 451
EP - 468
JO - Discrete and Continuous Dynamical Systems
JF - Discrete and Continuous Dynamical Systems
IS - 2
ER -