Number of the records: 1
Rigidity and flexibility of polynomial entropy
Title Rigidity and flexibility of polynomial entropy Author info Samuel Roth, Zuzana Roth ... [et al.] Author Roth Samuel (34%)
Co-authors Roth Zuzana (33%)
Snoha Ľubomír 1955- (33%) UMBFP10 - Katedra matematiky
Source document Advances in mathematics. Vol. 443 (2024), pp. 1-44. - Amsterdam : Elsevier B.V., 2024 Keywords entropia dendrity flexibilita - flexibility Form. Descr. články - journal articles Language English Country Netherlands Annotation We introduce the notion of a one-way horseshoe for topological dynamical systems and show that, quite surprisingly, it plays the same role in the theory of polynomial entropy as the notion of a horseshoe plays in the theory of topological entropy. Indeed, we show that the existence of a one-way horseshoe gives a lower bound for polynomial entropy and for maps of the interval also conversely, polynomial entropy is given by one-way horseshoes of iterates of the map, analogously to Misiurewicz's theorem on topological entropy and standard 'two-way' horseshoes. As a consequence we get a rigidity result that if the polynomial entropy of an interval map is finite, then it is an integer. Furthermore, for interval maps of Sharkovskii type 1 the polynomial entropy can also be computed by what we call chains of essential intervals. We further describe the possible values of polynomial entropy of maps of all Sharkovskii types. We then apply our tools to the classic logistic family, showing that the polynomial entropy increases weakly monotonically with the parameter, making discrete jumps up at bifurcation points along the perioddoubling cascade. On the other hand, we show that in the class of all continua the polynomial entropy of continuous maps is very flexible. For every value alpha is an element of [0, infinity] there is a homeomorphism on a continuum with polynomial entropy alpha. We discuss also possible values of the polynomial entropy of continuous maps on dendrites. URL Link na plný text Public work category ADC No. of Archival Copy 54847 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika 
article
Number of the records: 1