Kneading with weights

Abstract : We generalise Milnor-Thurston's kneading theory to the setting of piecewise continuous and monotone interval maps with weights. We define a weighted kneading determinant ${\cal D}(t)$ and establish combinatorially two kneading identities, one with the cutting invariant and one with the dynamical zeta function. For the pressure $\log \rho_1$ of the weighted system, playing the role of entropy, we prove that ${\cal D}(t)$ is non-zero when $|t|<1/\rho_1$ and has a zero at $1/\rho_1$. Furthermore, our map is semi-conjugate to an analytic family $h_t, 0 < t < 1/\rho_1$ of Cantor PL maps converging to an interval PL map $h_{1/\rho_1}$ with equal pressure
Type de document :
Pré-publication, Document de travail
25 pages, 3 figures. 2014
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Soumis le : dimanche 20 juillet 2014 - 14:00:01
Dernière modification le : mercredi 19 décembre 2018 - 14:08:04
Document(s) archivé(s) le : lundi 24 novembre 2014 - 20:48:03


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  • HAL Id : hal-01026144, version 1
  • ARXIV : 1407.5313


Hans Henrik Rugh, Lei Tan. Kneading with weights. 25 pages, 3 figures. 2014. 〈hal-01026144〉



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