Search results for " diffeomorphism"

showing 3 items of 13 documents

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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3-manifolds which are orbit spaces of diffeomorphisms

2008

Abstract In a very general setting, we show that a 3-manifold obtained as the orbit space of the basin of a topological attractor is either S 2 × S 1 or irreducible. We then study in more detail the topology of a class of 3-manifolds which are also orbit spaces and arise as invariants of gradient-like diffeomorphisms (in dimension 3). Up to a finite number of exceptions, which we explicitly describe, all these manifolds are Haken and, by changing the diffeomorphism by a finite power, all the Seifert components of the Jaco–Shalen–Johannson decomposition of these manifolds are made into product circle bundles.

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Seifert fibrationsClass (set theory)Pure mathematicsGradient-like diffeomorphism[ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS]Dimension (graph theory)[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]Space (mathematics)01 natural sciences[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesAttractorJaco–Shalen–Johannson decomposition0101 mathematicsFinite setMathematics::Symplectic Geometry[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]Mathematics010102 general mathematicsMathematical analysisMathematics::Geometric Topology3-manifoldsProduct (mathematics)010307 mathematical physicsGeometry and TopologyDiffeomorphismOrbit (control theory)
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Algebraic models of the real affine plane

2017

We introduce a new invariant, the real (logarithmic)-Kodaira dimension, that allows to distinguish smooth real algebraic surfaces up to birational diffeomorphism. As an application, we construct infinite families of smooth rational real algebraic surfaces with trivial homology groups, whose real loci are diffeomorphic to $\mathbb{R}^2$, but which are pairwise not birationally diffeomorphic. There are thus infinitely many non-trivial models of the real affine plane, contrary to the compact case.

birational diffeomorphismaffine complexificationMathematics::Algebraic Geometry14R05 14R25 14E05 14P25 14J26.affine surface[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]rational fibrationReal algebraic model[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]Mathematics::Symplectic Geometry[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]
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