**Authors:** Denis J. Evans, E. G. D. Cohen, Debra
J. Searles, F. Bonetto

**Title:** *Note on the Kaplan--Yorke dimension and
linear transport coefficients.*

**Abstract: **number of new relations between
the Kaplan--Yorke dimension, phase space contraction, transport coefficients
and the maximal Lyapunov exponents are given for dissipative thermostatted
systems, subject to a small but non-zero external field in a nonequilibrium
stationary state. A condition for the extensivity of phase space
dimension reduction is given. A new expression for the linear transport
coefficients in terms of the Kaplan--Yorke dimension is derived.
Alternatively, the Kaplan--Yorke dimension for a dissipative macroscopic
system can be expressed in terms of the linear transport coefficients of
the system. The agreement with computer simulations for an atomic
fluid at small shear rates is very good.

**Keywords:** dynamical systems, KY--dimension,
Lyapunov exponent, transport coefficient.

Denis J. Evans: Research School of Chemistry, The Australian
National University, Canberra, ACT 0200, Australia

E. G. D. Cohen: The Rockefeller University, 1230 York
Avenue, New York, NY 10021

Debra J. Searles: School of Science, Griffith University,
Nathan, Brisbane, Qld 4111, Australia

F. Bonetto: Department of Mathematics, Rutgers University,
New Brunswick, NJ 08903