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Название: Renormalization in the Henon Family, I: Universality But Non-Rigidity
Авторы: Carvalho A.D., Lyubich M., Martens M.
Journal of Statistical Physics, Vol. 121, Nos. 5/6, December 2005. p. 611-669.
In this paper geometric properties oi infinitely renormahzable real Henon-like maps F in R^2 are studied. It is shown that the appropriately defined renormal-izations R^n F converge exponentially to the one-dimensional renormalization fixed point. The convergence to one-dimensional systems is at a super-exponential rate controlled by the average Jacobian and a universal function a(x). It is also shown that the attracting Cantor set of such a map has Hausdorff dimension less than 1, but contrary to the one-dimensional intuition, it is not rigid, does not lie on a smooth curve, and generically has unbounded geometry.