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Entropy of $C^1$ diffeomorphisms without a dominated splitting

Entropy of $C^1$ diffeomorphisms without a dominated splitting

A classical construction due to Newhouse creates horseshoes from hyperbolic periodic orbits with large period and weak domination through local $C^1$-perturbations. Our main theorem shows that, when one works in the $C^1$ topology, the entropy of such horseshoes can be made arbitrarily close to an upper bound deriving from Ruelle's …