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- W2804080994 abstract "This note presents a non-rigorous study of the linear response for an SRB (or `natural physical') measure $rho$ of a diffeomorphism $f$ in the presence of tangencies of the stable and unstable manifolds of $rho$. We propose that generically, if $rho$ has no zero Lyapunov exponent, if its stable dimension is sufficiently large (greater than 1/2 or perhaps 3/2) and if it is exponentially mixing in a suitable sense, then the following formal expression for the first derivative of $rho(phi)$ with respect to $f$ along $X$ is convergent: $$ Psi(z)=sum_{n=0}^infty z^nintrho(dx),X(x)cdotnabla_x(phicirc f^n)qquad{rm for}qquad z=1 $$ This suggests that an SRB measure may exist for small perturbations of $f$, with weak differentiability." @default.
- W2804080994 created "2018-06-01" @default.
- W2804080994 creator A5018556476 @default.
- W2804080994 date "2018-11-15" @default.
- W2804080994 modified "2023-10-16" @default.
- W2804080994 title "Linear response theory for diffeomorphisms with tangencies of stable and unstable manifolds—a contribution to the Gallavotti–Cohen chaotic hypothesis" @default.
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- W2804080994 doi "https://doi.org/10.1088/1361-6544/aae740" @default.
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