28 research outputs found

    Creation of blenders in the conservative setting

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    In this work we prove that each C^r conservative diffeomorphism with a pair of hyperbolic periodic points of co-index one can be C^1-approximated by C^r conservative diffeomorphisms having a blender.Comment: 4 figures, 16 figure

    Removing zero Lyapunov exponents in volume-preserving flows

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    Baraviera and Bonatti proved that it is possible to perturb, in the c^1 topology, a volume-preserving and partial hyperbolic diffeomorphism in order to obtain a non-zero sum of all the Lyapunov exponents in the central direction. In this article we obtain the analogous result for volume-preserving flows.Comment: 10 page

    Dominated Splitting and Pesin's Entropy Formula

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    Let MM be a compact manifold and f:MMf:\,M\to M be a C1C^1 diffeomorphism on MM. If μ\mu is an ff-invariant probability measure which is absolutely continuous relative to Lebesgue measure and for μ\mu a.e.xM,a.\,\,e.\,\,x\in M, there is a dominated splitting Torb(x)M=EFT_{orb(x)}M=E\oplus F on its orbit orb(x)orb(x), then we give an estimation through Lyapunov characteristic exponents from below in Pesin's entropy formula, i.e., the metric entropy hμ(f)h_\mu(f) satisfies hμ(f)χ(x)dμ,h_{\mu}(f)\geq\int \chi(x)d\mu, where χ(x)=i=1dimF(x)λi(x)\chi(x)=\sum_{i=1}^{dim\,F(x)}\lambda_i(x) and λ1(x)λ2(x)...λdimM(x)\lambda_1(x)\geq\lambda_2(x)\geq...\geq\lambda_{dim\,M}(x) are the Lyapunov exponents at xx with respect to μ.\mu. Consequently, by using a dichotomy for generic volume-preserving diffeomorphism we show that Pesin's entropy formula holds for generic volume-preserving diffeomorphisms, which generalizes a result of Tahzibi in dimension 2

    Central Lyapunov exponent of partially hyperbolic diffeomorphisms of T3\mathbb T^{3}

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