0000000000277111

AUTHOR

Maciej P. Wojtkowski

showing 2 related works from this author

Homogeneous Weyl connections of non-positive curvature

2015

We study homogenous Weyl connections with non-positive sectional curvatures. The Cartesian product $\mathbb S^1 \times M$ carries canonical families of Weyl connections with such a property, for any Riemmanian manifold $M$. We prove that if a homogenous Weyl connection on a manifold, modeled on a unimodular Lie group, is non-positive in a stronger sense (streched non-positive), then it must be locally of the product type.

Mathematics - Differential GeometryPure mathematics01 natural sciencesGaussian thermostatssymbols.namesake0103 physical sciencesFOS: MathematicsNon-positive curvatureNon-positive curvature0101 mathematicsConnection (algebraic framework)53C24 53C21Mathematics010102 general mathematicsMathematical analysisLie groupWeyl connectionsCartesian productManifoldUnimodular matrixDifferential Geometry (math.DG)Differential geometrysymbolsWeyl transformationMathematics::Differential Geometry010307 mathematical physicsGeometry and TopologyAnalysisAnnals of Global Analysis and Geometry
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Integrability via Reversibility

2017

Abstract A class of left-invariant second order reversible systems with functional parameter is introduced which exhibits the phenomenon of robust integrability: an open and dense subset of the phase space is filled with invariant tori carrying quasi-periodic motions, and this behavior persists under perturbations within the class. Real-analytic volume preserving systems are found in this class which have positive Lyapunov exponents on an open subset, and the complement filled with invariant tori.

Pure mathematicsClass (set theory)Dense setGeneral Physics and AstronomyLyapunov exponentDynamical Systems (math.DS)IntegrabilityCoexistence of integrability and chaotic behavior01 natural sciencessymbols.namesakeReversibility0103 physical sciencesFOS: MathematicsOrder (group theory)0101 mathematicsInvariant (mathematics)Mathematics - Dynamical SystemsMathematical PhysicsMathematicsComplement (set theory)010102 general mathematicsTorusPhase spacesymbols010307 mathematical physicsGeometry and Topology
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