Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, EpiSciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [10 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01026144
Contributor : Lei Tan Connect in order to contact the contributor
Submitted on : Sunday, July 20, 2014 - 2:00:01 PM
Last modification on : Sunday, June 26, 2022 - 12:01:41 PM
Long-term archiving on: : Monday, November 24, 2014 - 8:48:03 PM

Files

kneading-shortversion.pdf
Files produced by the author(s)

Identifiers

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

Citation

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

Share

Metrics

Record views

240

Files downloads

112