Abstract
A natural definition of an attractor as an invariant measure is given (based on the ergodic theory of axiom A diffeomorphisms) and some results are proved which support this definition. It is also proved that if an attractor has every characteristic exponent less than zero in a set of nonzero measure, then the support set of the attractor is an asymptotic stable periodic orbit.
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de Oliveira, C.R. Attractors and characteristic exponents. J Stat Phys 53, 603–612 (1988). https://doi.org/10.1007/BF01014216
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DOI: https://doi.org/10.1007/BF01014216