363 research outputs found
Bootstrap for local rigidity of Anosov automorphisms on the 3-torus
We establish a strong form of local rigidity for hyperbolic automorphisms of
the 3-torus with real spectrum. Namely, let
be a hyperbolic automorphism of the 3-torus with real spectrum and let be a
small perturbation of . Then is smoothly () conjugate to
if and only if obstructions to conjugacy given by the eigenvalues at
periodic points of vanish. By combining our result and a local rigidity
result of Kalinin and Sadovskaya for conformal automorphisms this completes the
local rigidity program for hyperbolic automorphisms in dimension 3. Our work
extends de la Llave-Marco-Moriy\'on 2-dimensional local rigidity theory.Comment: 16 page
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