Stability of the topological pressure for piecewise monotonic maps underC1-perturbations

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) Assume thatX is a finite union of closed intervals and consider aC^sup 1^-mapX[arrow right] for which {cX: T'c=0} is finite. Set... Fix ann . For [epsi]>0, theC^sup 1^-map... is called an [epsi]-perturbation ofT if... is a piecewise monotonic map with at mostn intervals of monotonicity and... is [epsi]-close toT in theC^sup 1^-topology. The influence of small perturbations ofT on the dynamical system (R(T),T) is investigated. Under a certain condition on the continuous functionf:X [arrow right] , the topological pressure is lower semi-continuous. Furthermore, the topological pressure is upper semi-continuous for every continuous functionf:X [arrow right] . If (R(T),T) has positive topological entropy and a unique measure [mu] of maximal entropy, then every sufficiently small perturbation... ofT has a unique measure... of maximal entropy, and the map... is continuous atT in the weak star-topology.[PUBLICATION ABSTRACT]