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2.0

Jun 29, 2018
06/18

by
Wescley Bonomo; Jorge Rocha; Paulo Varandas

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In this paper we study the centralizer of flows and $\mathbb R^d$-actions on compact Riemannian manifolds. We prove that the centralizer of every $C^\infty$ Komuro-expansive flow with non-ressonant singularities is trivial, meaning it is the smallest possible, and deduce there exists an open and dense subset of geometric Lorenz attractors with trivial centralizer. We show that $\mathbb R^d$-actions obtained as suspension of $\mathbb Z^d$-actions are expansive if and only if the same holds for...

Topics: Dynamical Systems, Classical Analysis and ODEs, Mathematics

Source: http://arxiv.org/abs/1604.06516

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3.0

Jun 29, 2018
06/18

by
Jorge Rocha; Paulo Varandas

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In the late nineties, Smale proposed a list of problems for the next century and, among these, it was conjectured that for every $r\ge 1$ a $C^r$-generic diffeomorphism has trivial centralizer. Our contribution here is to prove the triviality of $C^r$-centralizers on hyperbolic basic sets. In particular, $C^r$-generic transitive Anosov diffeomorphisms have a trivial $C^1$-centralizer. These results follow from a more general criterium for expansive homeomorphisms with the gluing orbit property....

Topics: Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1606.00132

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50

Sep 23, 2013
09/13

by
Mario Bessa; Jorge Rocha

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We prove that the C1-interior of the set of all topologically stable C1-incompressible flows is contained in the set of Anosov incompressible flows. Moreover, we obtain an analogous result for the discrete-time case.

Source: http://arxiv.org/abs/1006.3725v1

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50

Sep 22, 2013
09/13

by
Mario Bessa; Jorge Rocha

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We prove that the C1 interior of the set of all topologically stable C1 symplectomorphisms is contained in the set of Anosov symplectomorphisms.

Source: http://arxiv.org/abs/1101.5128v1

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49

Sep 23, 2013
09/13

by
Mario Bessa; Jorge Rocha

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We prove the following dichotomy for vector fields in a C1-residual subset of volume-preserving flows: for Lebesgue almost every point all Lyapunov exponents equal to zero or its orbit has a dominated splitting. As a consequence if we have a vector field in this residual that cannot be C1-approximated by a vector field having elliptic periodic orbits, then, there exists a full measure set such that every orbit of this set admits a dominated splitting for the linear Poincare flow. Moreover, we...

Source: http://arxiv.org/abs/0810.3855v1

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50

Sep 19, 2013
09/13

by
Mario Bessa; Jorge Rocha

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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.

Source: http://arxiv.org/abs/math/0610558v1

4
4.0

Apr 21, 2021
04/21

by
Jorge Rocha (jasrocha)

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Customized version of http://www.thingiverse.com/thing:256658 Created with Customizer! http://www.thingiverse.com/apps/customizer/run?thing_id=256658

Topics: Coins & Badges, thingiverse, stl, customized

2
2.0

Apr 16, 2021
04/21

by
Jorge Rocha (jasrocha)

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apito

Topics: thingiverse, Toys & Games, stl

2
2.0

Apr 16, 2021
04/21

by
Jorge Rocha (jasrocha)

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Customized version of http://www.thingiverse.com/thing:923244 Created with Customizer! http://www.thingiverse.com/apps/customizer/run?thing_id=923244

Topics: customized, thingiverse, 3D Printing, stl

8
8.0

Jun 27, 2018
06/18

by
Mario Bessa; Jorge Rocha; Paulo Varandas

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In this paper we revisit uniformly hyperbolic basic sets and the domination of Oseledets splittings at periodic points. We prove that periodic points with simple Lyapunov spectrum are dense in non-trivial basic pieces of Cr-residual diffeomorphisms on three-dimensional manifolds (r >= 1). In the case of the C1-topology we can prove that either all periodic points of a hyperbolic basic piece for a diffeomorphism f have simple spectrum C1- robustly (in which case f has a finest dominated...

Topics: Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1506.04677

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36

Sep 19, 2013
09/13

by
Mario Bessa; Celia Ferreira; Jorge Rocha

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A Hamiltonian level, say a pair $(H,e)$ of a Hamiltonian $H$ and an energy $e \in \mathbb{R}$, is said to be Anosov if there exists a connected component $\mathcal{E}_{H,e}$ of $H^{-1}({e})$ which is uniformly hyperbolic for the Hamiltonian flow $X_H^t$. The pair $(H,e)$ is said to be a Hamiltonian star system if there exists a connected component $\mathcal{E}^\star_{H,e}$ of the energy level $H^{-1}({{e}})$ such that all the closed orbits and all the critical points of...

Source: http://arxiv.org/abs/0909.3801v1

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4.0

Jun 29, 2018
06/18

by
Jorge Rocha; Paulo Varandas

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In this paper we study $C^1$-structurally stable diffeomorphisms, that is, $C^1$ Axiom A diffeomorphisms with the strong transversality condition. In contrast to the case of dynamics restricted to a hyperbolic basic piece, structurally stable diffeomorphisms are in general not expansive and the conjugacies between $C^1$-close structurally stable diffeomorphisms may be non-unique, even if there are assumed $C^0$-close to the identity. Here we give a necessary and sufficient condition for a...

Topics: Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1605.06864

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118

Jul 20, 2013
07/13

by
Mario Bessa; Celia Ferreira; Jorge Rocha

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In this paper we contribute to the generic theory of Hamiltonians by proving that there is a C2-residual R in the set of C2 Hamiltonians on a closed symplectic manifold M, such that, for any H in R, there is an open and dense set S(H) in H(M) such that, for every e in S(H), the Hamiltonian level (H,e) is topologically mixing.

Source: http://arxiv.org/abs/1203.3849v1

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316

Sep 18, 2014
09/14

by
Chiara Barbieri; Mário Vicente; Sandra Oliveira; Koen Bostoen; Jorge Rocha; Mark Stoneking; Brigitte Pakendorf

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Bantu speech communities expanded over large parts of sub-Saharan Africa within the last 4000-5000 years, reaching different parts of southern Africa 1200-2000 years ago. The Bantu languages subdivide in several major branches, with languages belonging to the Eastern and Western Bantu branches spreading over large parts of Central, Eastern, and Southern Africa. There is still debate whether this linguistic divide is correlated with a genetic distinction between Eastern and Western Bantu...

Topic: Evolutionary Biology

Source: http://biorxiv.org/content/early/2014/02/18/002808

4
4.0

Apr 21, 2021
04/21

by
Jorge Rocha (jasrocha)

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Customized version of http://www.thingiverse.com/thing:1143325 Created with Customizer! http://www.thingiverse.com/apps/customizer/run?thing_id=1143325

Topics: thingiverse, stl, Office, customized

2
2.0

Apr 16, 2021
04/21

by
Jorge Rocha (jasrocha)

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Customized version of http://www.thingiverse.com/thing:923244 Created with Customizer! http://www.thingiverse.com/apps/customizer/run?thing_id=923244

Topics: customized, thingiverse, 3D Printing, stl

2
2.0

Apr 16, 2021
04/21

by
Jorge Rocha (jasrocha)

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Customized version of http://www.thingiverse.com/thing:46825 Created with Customizer! http://www.thingiverse.com/apps/customizer/run?thing_id=46825

Topics: Math, customized, thingiverse, stl