Yunping Jiang and David Ruelle 2005 Nonlinearity 18 2447 doi:10.1088/0951-7715/18/6/002
Analyticity of the susceptibility function for unimodal Markovian maps of the interval
Yunping Jiang1,3 and David Ruelle2,4
Show affiliationsRecommended by K M Khanin
We study the expression (susceptibility) ![\[
\begin{equation*}\Psi(\lambda)=\sum_{n=0}^\infty\lambda^n\int_I\!\rho(\rmd
x)X(x){\frac{\rmd}{\rmd x}}(A(f^nx)),\end{equation*}
\]](http://ej.iop.org/images/0951-7715/18/6/002/non192835ude001.gif)
where f is a unimodal Markovian map of the interval I, ρ = ρf is the corresponding absolutely continuous invariant measure and A is a C1 function defined on I. We show that Ψ(λ) is analytic near λ = 1, where Ψ(1) is formally the derivative of 
with respect to f in the direction of the vector field X.
- PACS
-
02.30.-f Function theory, analysis
02.50.-r Probability theory, stochastic processes, and statistics
- MSC
-
37C40 Smooth ergodic theory, invariant measures (See also 37Dxx)
37C10 Vector fields, flows, ordinary differential equations
37E05 Maps of the interval (piecewise continuous, continuous, smooth)
- Subjects
- Dates
-
Issue 6 (November 2005)
Received 11 January 2005, in final form 3 July 2005
Published 8 August 2005
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Analyticity of the susceptibility function for unimodal Markovian maps of the interval
Yunping Jiang and David Ruelle 2005 Nonlinearity 18 2447
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