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We consider groups generated by real analytic diffeomorphisms of a compact manifold close to the identity. We show that the dynamics of such a group is recurrent unless the group satisfies a very particular property, similar to solvability. We study in detail the case of diffeomorphisms of the...
In this paper we construct stable and unstable foliations for expansive flows operating on 3-manifolds. We also prove that the fundamental group of the manifold has exponential growth.
We consider smooth families of diffeomorphisms of the circle. We prove that the set of parameter values which correspond to non-linearizable maps with irrational rotation numbers is of Hausdorff dimension 0.
We give a complete classification in the smooth category of local phase portraits (near the origin) of generic constrained systems of the formA(x)x=f(x), wherex ∈ ℝ2,A(x) is a 2×2 matrix-valued function,f is a vector field, the origin is an impasse point (detA(0)=0, and the existence and the...
We show here that by modifying the eigenvalues λ2 < λ3 < 0 < λ1 of the geometric Lorenz attractor, replacing the usualexpanding condition λ3+λ1 > 0 by acontracting condition λ3+λ1 < 0, we can obtain vector fields exhibiting transitive non-hyperbolic attractors which are persistent in the...
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