Search results for " 37D30"

showing 4 items of 14 documents

Periodic measures and partially hyperbolic homoclinic classes

2019

In this paper, we give a precise meaning to the following fact, and we prove it: $C^1$-open and densely, all the non-hyperbolic ergodic measures generated by a robust cycle are approximated by periodic measures. We apply our technique to the global setting of partially hyperbolic diffeomorphisms with one dimensional center. When both strong stable and unstable foliations are minimal, we get that the closure of the set of ergodic measures is the union of two convex sets corresponding to the two possible $s$-indices; these two convex sets intersect along the closure of the set of non-hyperbolic ergodic measures. That is the case for robustly transitive perturbation of the time one map of a tr…

Pure mathematicsMathematics::Dynamical SystemsGeneral MathematicsClosure (topology)Dynamical Systems (math.DS)01 natural sciencespartial hyperbolicityquasi-hyperbolic stringBlenderFOS: Mathematicsnon-hyperbolic measureErgodic theoryHomoclinic orbitMathematics - Dynamical Systems0101 mathematics[MATH]Mathematics [math]ergodic measureperiodic measureMathematicsfoliationsTransitive relationApplied MathematicsMSC (2010): Primary 37D30 37C40 37C50 37A25 37D25010102 general mathematicsRegular polygonTorusstabilityFlow (mathematics)systemsDiffeomorphismrobust cycleLyapunov exponent
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Seifert manifolds admitting partially hyperbolic diffeomorphisms

2017

We characterize which 3-dimensional Seifert manifolds admit transitive partially hyperbolic diffeomorphisms. In particular, a circle bundle over a higher-genus surface admits a transitive partially hyperbolic diffeomorphism if and only if it admits an Anosov flow.

Surface (mathematics)Pure mathematicsMathematics::Dynamical SystemsCircle bundle[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]Dynamical Systems (math.DS)01 natural sciences[MATH.MATH-GN]Mathematics [math]/General Topology [math.GN]0103 physical sciencesFOS: MathematicsMSC: Primary: 37D30 37C15; Secondary: 57R30 55R05.Mathematics - Dynamical Systems0101 mathematicsMathematics::Symplectic GeometrySeifert spacesMathematics - General TopologyMathematicsTransitive relationAlgebra and Number TheoryApplied Mathematics010102 general mathematicsGeneral Topology (math.GN)Mathematics::Geometric TopologyFlow (mathematics)Partially hyperbolic diffeomorphisms010307 mathematical physicsDiffeomorphismAnalysis
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Dirac physical measures for generic diffeomorphisms

2016

We prove that, for a $C^1$ generic diffeomorphism, the only Dirac physical measures with dense statistical basin are those supported on sinks.

Theoretical computer scienceGeneral Mathematics[ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS]010102 general mathematicsDirac (software)[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]Generic diffeomorphismsMSC: 37C05 37C20 37D30Dynamical Systems (math.DS)01 natural sciencesComputer Science ApplicationsPhysical measures0103 physical sciencesFOS: Mathematics010307 mathematical physicsDiffeomorphismMathematics - Dynamical Systems0101 mathematicsPhysics::Atmospheric and Oceanic PhysicsMathematicsMathematical physics
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Robust existence of nonhyperbolic ergodic measures with positive entropy and full support

2021

We prove that for some manifolds $M$ the set of robustly transitive partially hyperbolic diffeomorphisms of $M$ with one-dimensional nonhyperbolic centre direction contains a $C^1$-open and dense subset of diffeomorphisms with nonhyperbolic measures which are ergodic, fully supported and have positive entropy. To do so, we formulate abstract conditions sufficient for the construction of an ergodic, fully supported measure $\mu$ which has positive entropy and is such that for a continuous function $\phi\colon X\to\mathbb{R}$ the integral $\int\phi\,d\mu$ vanishes. The criterion is an extended version of the control at any scale with a long and sparse tail technique coming from the previous w…

Transitive relationPure mathematicsHyperbolicityMathematics::Dynamical SystemsDense setContinuous function (set theory)[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]Scale (descriptive set theory)Dynamical Systems (math.DS)Measure (mathematics)Theoretical Computer SciencePositive entropyMathematics (miscellaneous)FOS: MathematicsErgodic theory37D25 37D35 37D30 28D99Mathematics - Dynamical SystemsMathematicsCriterion
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