000128120 001__ 128120
000128120 005__ 20190509132211.0
000128120 0247_ $$2doi$$a10.5075/epfl-thesis-4232
000128120 02470 $$2urn$$aurn:nbn:ch:bel-epfl-thesis4232-7
000128120 02471 $$2nebis$$a5665661
000128120 037__ $$aTHESIS
000128120 041__ $$aeng
000128120 088__ $$a4232
000128120 245__ $$aContribution to the ergodic theory of piecewise monotone continuous maps
000128120 269__ $$a2008
000128120 260__ $$bEPFL$$c2008$$aLausanne
000128120 300__ $$a107
000128120 336__ $$aTheses
000128120 520__ $$aThis thesis is devoted to the ergodic theory of the piecewise monotone continuous maps of the interval. The coding is a classical approach for these maps. Thanks to the coding, we get a symbolic dynamical system which is almost isomorphic to the initial dynamical system. The principle of the coding is very similar to the one of expansion of real numbers. We first define the coding in a perspective similar to the one of the expansions of real numbers; this perspective was already adopted by Rényi and Parry in their papers about the expansions of numbers. Then we present the theory of Hofbauer about the links between the ergodic properties of a piecewise monotone continuous map of the interval and the corresponding symbolic dynamical system. We prove that there is a bijection between the sets of measures of maximal entropy of these two dynamical systems. We apply these results to the study of two families of maps: first the maps Tα,β(x) := βx + α mod 1, then the maps we will call generalized β-transformations. For the family of maps Tα,β, we describe in detail the family of symbolic dynamical systems obtained by the coding. Then we turn to the question of normality of the orbits for the maps Tα,β. Finally we study the generalized β-transformations: we prove that most of them have a a unique measure of maximal entropy, then we also study the normality of the orbits for theses maps.
000128120 6531_ $$amaps of the interval
000128120 6531_ $$asymbolic dynamic
000128120 6531_ $$aexpansion of numbers
000128120 6531_ $$atopological entropy
000128120 6531_ $$aMarkov diagram
000128120 6531_ $$anormal numbers
000128120 6531_ $$aapplications de l'intervalle
000128120 6531_ $$adynamique symbolique
000128120 6531_ $$adéveloppement des nombres
000128120 6531_ $$aentropie topologique
000128120 6531_ $$adiagramme de Markov
000128120 6531_ $$anombres normaux
000128120 700__ $$aFaller, Bastien
000128120 720_2 $$aPfister, Charles-Edouard$$edir.$$g106090$$0243461
000128120 8564_ $$uhttps://infoscience.epfl.ch/record/128120/files/EPFL_TH4232.pdf$$zTexte intégral / Full text$$s1649411$$yTexte intégral / Full text
000128120 909C0 $$xU10947$$0252205$$pGR-PF
000128120 909CO $$pthesis-bn2018$$pDOI$$pSB$$ooai:infoscience.tind.io:128120$$qDOI2$$qGLOBAL_SET$$pthesis
000128120 918__ $$dEDMA$$cIACS$$aSB
000128120 919__ $$aGR-PF
000128120 920__ $$b2008
000128120 970__ $$a4232/THESES
000128120 973__ $$sPUBLISHED$$aEPFL
000128120 980__ $$aTHESIS