Geodesic
Niding designs of models of constant inclination for generalized shifts of a segment
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 19 (2017) no. 2, pp. 85-90.

Voir la notice de l'article provenant de la source Math-Net.Ru

For one-dimensional discontinuous maps with zero topological entropy we apply the technique of kneading invariants and kneading series. The kneading technique was introduced first by J. Milnor and W. Thurston for continuous piecewise monotonic one-dimensional maps and was applied to maps with positive topological entropy. In the present paper we show that by approaching the zero entropy one using kneading series may define invariant measure for generalized interval exchange transformations and also for a class of discontinuous maps without periodic points. Thus, in terms of kneading series we construct a semiconjugacy (being actually a conjugacy in the transitive case) with a model map of unit (in absolute value) slope. The proposed construction is determined by formulas which allow to calculate the parameters of the model map with required accuracy.
Keywords: kneading series, generalized interval exchange transformations, topological entropy. 
@article{SVMO_2017_19_2_a6,
     author = {M. I. Malkin and K. A. Saphonov},
     title = {Niding designs of models of constant inclination for generalized shifts of a segment},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {85--90},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2017_19_2_a6/}
}
TY  - JOUR
AU  - M. I. Malkin
AU  - K. A. Saphonov
TI  - Niding designs of models of constant inclination for generalized shifts of a segment
JO  - Žurnal Srednevolžskogo matematičeskogo obŝestva
PY  - 2017
SP  - 85
EP  - 90
VL  - 19
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SVMO_2017_19_2_a6/
LA  - ru
ID  - SVMO_2017_19_2_a6
ER  - 
%0 Journal Article
%A M. I. Malkin
%A K. A. Saphonov
%T Niding designs of models of constant inclination for generalized shifts of a segment
%J Žurnal Srednevolžskogo matematičeskogo obŝestva
%D 2017
%P 85-90
%V 19
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SVMO_2017_19_2_a6/
%G ru
%F SVMO_2017_19_2_a6
M. I. Malkin; K. A. Saphonov. Niding designs of models of constant inclination for generalized shifts of a segment. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 19 (2017) no. 2, pp. 85-90. http://geodesic.mathdoc.fr/item/SVMO_2017_19_2_a6/

[1] M. I. Malkin, K. A. Safonov, “The application of niding-series for the semi-conjugation of Lorentz mappings with zero entropy”, Zhurnal Srednevolzhskogo matematicheskogo obshchestva, 18:4 (2016), 34–40 (In Russ) | MR

[2] J. Milnor, W. Thurston, On iterated maps of the interval, preprint, 1977 | MR

[3] M. I. Malkin, “Piecewise-linear models for mappings of the Lorentz type”, Methods of the qualitative theory of differential equations, Interuniversity. Sat. Sci. Tr., ed. E.A. Leontovich – Andronova, GGU publ., Gorky, 1987 (In Russ) | MR

[4] J. Buzzi, P. Hubert, “Piecewise monotone maps without periodic points: rigity, measures and complexity”, Ergod. Th. Dynam. Sys., 24 (2004), 383–405 | DOI | MR | Zbl

[5] W. de Melo, S. Van Strien, One dimensional dynamics, Springer, Berlin, 1993 | MR | Zbl

[6] L. S. Young, “On the prevalence of horseshoes”, Trans. AMS, 263 (1981), 75–88 | DOI | MR | Zbl

[7] P. Fatou, “Series trigonometriques et series de Taylor”, Acta math., 30 (1906), 335–400 | DOI | MR | Zbl