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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
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https://hal.archives-ouvertes.fr/hal-01026144
Contributor : Lei Tan <>
Submitted on : Sunday, July 20, 2014 - 2:00:01 PM
Last modification on : Wednesday, September 16, 2020 - 4:05:25 PM
Long-term archiving on: : Monday, November 24, 2014 - 8:48:03 PM

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

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Hans Henrik Rugh, Lei Tan. Kneading with weights. 2014. ⟨hal-01026144⟩

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