Beiträge zur Algebra und Geometrie, ISSN 2191-0383, 2018, Volume 60, Issue 3, pp. 445 - 458

The aim of this paper is to construct a 1-parameter family of Sasakian manifold starting from a single Sasakian manifold. Concrete examples are given.

Geometry | Algebra | Convex and Discrete Geometry | Kählerian manifolds | 53C55 | Product manifolds | Algebraic Geometry | Mathematics | 53C15 | 53D25 | 53C25 | Sasakian manifolds

Geometry | Algebra | Convex and Discrete Geometry | Kählerian manifolds | 53C55 | Product manifolds | Algebraic Geometry | Mathematics | 53C15 | 53D25 | 53C25 | Sasakian manifolds

Journal Article

Mathematische Annalen, ISSN 0025-5831, 4/2018, Volume 370, Issue 3, pp. 1883 - 1907

Inspired by Katok’s examples of Finsler metrics with a small number of closed geodesics, we present two results on Reeb flows with finitely many periodic...

Mathematics, general | Mathematics | 53D25 | 53D35 | 37J55 | 37J45 | MATHEMATICS | ORBIT | CONTACT

Mathematics, general | Mathematics | 53D25 | 53D35 | 37J55 | 37J45 | MATHEMATICS | ORBIT | CONTACT

Journal Article

Journal of mathematical physics, ISSN 1089-7658, 2016, Volume 57, Issue 10, p. 102901

The Maupertuis principle allows us to regard classical trajectories as reparametrized geodesics of the Jacobi-Maupertuis (JM) metric on configuration space. We...

DYNAMICS | PHYSICS, MATHEMATICAL | SYZYGIES | Singularities | Energy | Quotients | Lagrangian equilibrium points | Geodesy | Configurations | Curvature | Collision dynamics | Three body problem

DYNAMICS | PHYSICS, MATHEMATICAL | SYZYGIES | Singularities | Energy | Quotients | Lagrangian equilibrium points | Geodesy | Configurations | Curvature | Collision dynamics | Three body problem

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 12/2017, Volume 191, Issue 1, pp. 1 - 35

We exhibit a class of Schottky subgroups of $$\mathbf {PU}(1,n)$$ PU ( 1 , n ) ( $$n \ge 2$$ n ≥ 2 ) which we call well-positioned and show that the Hausdorff...

Geometry | Dimension theory | Hausdorff dimension | 37D40 | Complex hyperbolic geometry | Non-conformal repellers | 37C45 | 28A80 | Mathematics | 53D25 | MATHEMATICS | INVARIANT | EXPONENT | ENTROPY | Mathematics - Dynamical Systems

Geometry | Dimension theory | Hausdorff dimension | 37D40 | Complex hyperbolic geometry | Non-conformal repellers | 37C45 | 28A80 | Mathematics | 53D25 | MATHEMATICS | INVARIANT | EXPONENT | ENTROPY | Mathematics - Dynamical Systems

Journal Article

Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, 02/2019, Volume 62, Issue 1, pp. 61 - 95

Given a smooth compact surface without focal points and of higher genus, it is shown that its geodesic flow is semi-conjugate to a continuous expansive flow...

2010 Mathematics subject classification: Primary 53D25 53C22 37D40 37D25 37D35 28D20 28D99 | expansive flow | MATHEMATICS | MAXIMAL ENTROPY | COMPACT SURFACES | conjugate points | focal points | time-preserving semi-conjugacy | measure of maximal entropy | MANIFOLDS | geodesic flow | UNIQUENESS | Parameterization | Conjugation

2010 Mathematics subject classification: Primary 53D25 53C22 37D40 37D25 37D35 28D20 28D99 | expansive flow | MATHEMATICS | MAXIMAL ENTROPY | COMPACT SURFACES | conjugate points | focal points | time-preserving semi-conjugacy | measure of maximal entropy | MANIFOLDS | geodesic flow | UNIQUENESS | Parameterization | Conjugation

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 06/2000, Volume 103, Issue 2, pp. 191 - 213

Journal Article

Mathematische Annalen, ISSN 0025-5831, 12/2014, Volume 360, Issue 3, pp. 995 - 1020

We prove lower bounds on the growth of certain filtered Hopf algebras by means of a Poincaré–Birkhoff–Witt type theorem for ordered products of primitive...

57T25 | Mathematics, general | 37C35 | Mathematics | 53D25 | Primary 16T05 | Secondary 37B40 | MATHEMATICS | VOLUME GROWTH | COMPLEX | FLOWS | TOPOLOGICAL-ENTROPY | Algebra

57T25 | Mathematics, general | 37C35 | Mathematics | 53D25 | Primary 16T05 | Secondary 37B40 | MATHEMATICS | VOLUME GROWTH | COMPLEX | FLOWS | TOPOLOGICAL-ENTROPY | Algebra

Journal Article

Letters in mathematical physics, ISSN 1573-0530, 2018, Volume 109, Issue 5, pp. 1219 - 1245

Earlier the theory of finite-gap integration was successfully applied to finite-component systems only. In this paper, we consider a first example of...

37J35 | 37K05 | Theoretical, Mathematical and Computational Physics | Complex Systems | Three-dimensional quasilinear systems of first order | 70H05 | 53D25 | Integrable dispersive chains | Physics | 37K10 | Geometry | Multi-phase solutions | Group Theory and Generalizations | REDUCTIONS | MAPS | ENERGY-DEPENDENT POTENTIALS | EQUATIONS | SYSTEMS | PHYSICS, MATHEMATICAL | SCHRODINGER-OPERATORS | Physics - Exactly Solvable and Integrable Systems

37J35 | 37K05 | Theoretical, Mathematical and Computational Physics | Complex Systems | Three-dimensional quasilinear systems of first order | 70H05 | 53D25 | Integrable dispersive chains | Physics | 37K10 | Geometry | Multi-phase solutions | Group Theory and Generalizations | REDUCTIONS | MAPS | ENERGY-DEPENDENT POTENTIALS | EQUATIONS | SYSTEMS | PHYSICS, MATHEMATICAL | SCHRODINGER-OPERATORS | Physics - Exactly Solvable and Integrable Systems

Journal Article

9.
Full Text
On local description of two-dimensional geodesic flows with a polynomial first integral

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 03/2016, Volume 49, Issue 17, p. 175201

In this paper we present a construction of multiparametric families of two-dimensional metrics with a polynomial first integral of arbitrary degree in momenta....

37J35 | geodesic flows | 37K05 | integrability | 70H05 | generalized hodograph method Mathematics Subject Classification: 53D25 | 37K10 | generalized hodograph method | PHYSICS, MULTIDISCIPLINARY | DYNAMICAL-SYSTEMS | EQUATIONS | HYDRODYNAMIC TYPE | CONSERVATION-LAWS | 2-TORUS | PHYSICS, MATHEMATICAL

37J35 | geodesic flows | 37K05 | integrability | 70H05 | generalized hodograph method Mathematics Subject Classification: 53D25 | 37K10 | generalized hodograph method | PHYSICS, MULTIDISCIPLINARY | DYNAMICAL-SYSTEMS | EQUATIONS | HYDRODYNAMIC TYPE | CONSERVATION-LAWS | 2-TORUS | PHYSICS, MATHEMATICAL

Journal Article

Regular and Chaotic Dynamics, ISSN 1560-3547, 11/2018, Volume 23, Issue 6, pp. 685 - 694

We give a new proof of the existence of compact surfaces embedded in ℝ3 with Anosov geodesic flows. This proof starts with a noncompact model surface whose...

embedded surfaces | cone fields | Anosov flow | 37D40 | 37D20 | Mathematics | 53D25 | Dynamical Systems and Ergodic Theory | geodesic flow | MATHEMATICS, APPLIED | MECHANICS | PHYSICS, MATHEMATICAL | Mathematics - Dynamical Systems

embedded surfaces | cone fields | Anosov flow | 37D40 | 37D20 | Mathematics | 53D25 | Dynamical Systems and Ergodic Theory | geodesic flow | MATHEMATICS, APPLIED | MECHANICS | PHYSICS, MATHEMATICAL | Mathematics - Dynamical Systems

Journal Article

Regular and Chaotic Dynamics, ISSN 1560-3547, 11/2015, Volume 20, Issue 6, pp. 729 - 738

Geodesics on SO(3) are characterized by constant angular velocity motions and as great circles on a three-sphere. The former interpretation is widely used in...

quaternions | geodesics | 70E40 | Mathematics | 53D25 | Dynamical Systems and Ergodic Theory | Listing’s law | constraints | Slerp | MATHEMATICS, APPLIED | MECHANICS | DYNAMICS | PHYSICS, MATHEMATICAL | BODY | Listing's law | KINEMATICS | Sphere | Mathematical research | Research

quaternions | geodesics | 70E40 | Mathematics | 53D25 | Dynamical Systems and Ergodic Theory | Listing’s law | constraints | Slerp | MATHEMATICS, APPLIED | MECHANICS | DYNAMICS | PHYSICS, MATHEMATICAL | BODY | Listing's law | KINEMATICS | Sphere | Mathematical research | Research

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 4/2018, Volume 110, Issue 4, pp. 391 - 402

We prove that if two non-trapping obstacles in $$\mathbb {R}^n$$ Rn satisfy some rather weak non-degeneracy conditions and the scattering rays in their...

Scattering length spectrum | 37D40 | 37D20 | Scattering by obstacles | 58J50 | Mathematics, general | Travelling time | Mathematics | 53D25 | Billiard trajectory | MATHEMATICS | SINGULARITIES | BOUNDARY-VALUE-PROBLEMS | TRAVELING TIMES | LENGTH SPECTRUM

Scattering length spectrum | 37D40 | 37D20 | Scattering by obstacles | 58J50 | Mathematics, general | Travelling time | Mathematics | 53D25 | Billiard trajectory | MATHEMATICS | SINGULARITIES | BOUNDARY-VALUE-PROBLEMS | TRAVELING TIMES | LENGTH SPECTRUM

Journal Article

Mathematical physics, analysis, and geometry, ISSN 1572-9656, 2018, Volume 21, Issue 2, pp. 1 - 9

In this short note we contribute to the generic dynamics of geodesic flows associated to metrics on compact Riemannian manifolds of dimension ≥ 2. We prove...

Residual sets | Theoretical, Mathematical and Computational Physics | 53D25 | Physics | Geometry | Expansiveness | 37D40 | Anosov | 37C20 | Analysis | Geodesic flows | Group Theory and Generalizations | Applications of Mathematics | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL

Residual sets | Theoretical, Mathematical and Computational Physics | 53D25 | Physics | Geometry | Expansiveness | 37D40 | Anosov | 37C20 | Analysis | Geodesic flows | Group Theory and Generalizations | Applications of Mathematics | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL

Journal Article

Journal of fixed point theory and applications, ISSN 1661-7746, 2016, Volume 19, Issue 1, pp. 175 - 204

We give a sharp lower bound for the number of geometrically distinct contractible periodic orbits of dynamically convex Reeb flows on prequantizations of...

Mathematical Methods in Physics | periodic orbits | contact homology | Analysis | dynamical convexity | 53D42 | Mathematics, general | Mathematics | 53D25 | 37J55 | Reeb flows | 37J45 | MATHEMATICS, APPLIED | CLOSED GEODESICS | EQUATIONS | MATHEMATICS | ENERGY SURFACES | FINSLER SPHERES | CONLEY CONJECTURE | FLOWS | REEB ORBITS | MASLOV INDEX | Orbits | Numerical analysis

Mathematical Methods in Physics | periodic orbits | contact homology | Analysis | dynamical convexity | 53D42 | Mathematics, general | Mathematics | 53D25 | 37J55 | Reeb flows | 37J45 | MATHEMATICS, APPLIED | CLOSED GEODESICS | EQUATIONS | MATHEMATICS | ENERGY SURFACES | FINSLER SPHERES | CONLEY CONJECTURE | FLOWS | REEB ORBITS | MASLOV INDEX | Orbits | Numerical analysis

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 4/2013, Volume 208, Issue 1, pp. 255 - 274

We analyze the extendability of the solutions to a certain second order differential equation on a Riemannian manifold (M, g), which is defined by a general...

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | MATHEMATICS, APPLIED | MECHANICS | Archives

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | MATHEMATICS, APPLIED | MECHANICS | Archives

Journal Article

Demonstratio Mathematica, ISSN 0420-1213, 09/2017, Volume 50, Issue 1, pp. 231 - 238

In this work we consider a class of contact manifolds (M, η) with an associated almost contact metric Structure (ϕ, ξ, η, g). This class contains, for example,...

Chinea-Gonzalez classification | contact manifold | 53D10 | 53D15 | 53D25 | 53C15 | almost contact metric structure | Chinea-gonzalez classication | Contact manifold | Almost contact metric structure

Chinea-Gonzalez classification | contact manifold | 53D10 | 53D15 | 53D25 | 53C15 | almost contact metric structure | Chinea-gonzalez classication | Contact manifold | Almost contact metric structure

Journal Article

Geometriae dedicata, ISSN 1572-9168, 2014, Volume 174, Issue 1, pp. 105 - 120

We study non-degenerate Reeb flows arising from perfect contact forms, i.e., the forms with vanishing contact homology differential. In particular, we obtain...

Geometry | Contact forms | Contact homology | Periodic orbits | 53D42 | Mathematics | 53D25 | 70H12 | Reeb flows | 37J45 | CONTACT | PERIODIC POINTS | MATHEMATICS | CLOSED CHARACTERISTICS | RESONANCE | ORBITS | DYNAMICS | HOMOLOGY | MORSE-THEORY

Geometry | Contact forms | Contact homology | Periodic orbits | 53D42 | Mathematics | 53D25 | 70H12 | Reeb flows | 37J45 | CONTACT | PERIODIC POINTS | MATHEMATICS | CLOSED CHARACTERISTICS | RESONANCE | ORBITS | DYNAMICS | HOMOLOGY | MORSE-THEORY

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 12/2012, Volume 161, Issue 1, pp. 51 - 61

We extend the Besicovitch-Federer projection theorem to transversal families of mappings. As an application we show that on a certain class of Riemann surfaces...

Geometry | Hausdorff dimension | Invariant measure | 37D20 | 28A80 | 37C45 | Projection | Mathematics | 53D25 | Unrectifiability | Geodesic flow | MATHEMATICS | Probability

Geometry | Hausdorff dimension | Invariant measure | 37D20 | 28A80 | 37C45 | Projection | Mathematics | 53D25 | Unrectifiability | Geodesic flow | MATHEMATICS | Probability

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 8/2016, Volume 346, Issue 1, pp. 1 - 34

Let M be a pinched negatively curved Riemannian manifold, whose unit tangent bundle is endowed with a Gibbs measure m F associated with a potential F. We...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | GEODESICS | PHYSICS, MATHEMATICAL | CURVED MANIFOLDS | FOLIATION

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | GEODESICS | PHYSICS, MATHEMATICAL | CURVED MANIFOLDS | FOLIATION

Journal Article

Regular and Chaotic Dynamics, ISSN 1560-3547, 11/2015, Volume 20, Issue 6, pp. 667 - 678

The magnetic geodesic flow on a flat two-torus with the magnetic field F = cos(x)dx ∧ dy is completely integrated and the description of all contractible...

37J35 | magnetic geodesic flow | Mathematics | 53D25 | integrable system | Dynamical Systems and Ergodic Theory | EXISTENCE | PERIODIC-ORBITS | FIELDS | MATHEMATICS, APPLIED | MECHANICS | PHYSICS, MATHEMATICAL | EXTREMALS | Research | Torus (Geometry) | Engineering research | Magnetic fields | Mathematical research

37J35 | magnetic geodesic flow | Mathematics | 53D25 | integrable system | Dynamical Systems and Ergodic Theory | EXISTENCE | PERIODIC-ORBITS | FIELDS | MATHEMATICS, APPLIED | MECHANICS | PHYSICS, MATHEMATICAL | EXTREMALS | Research | Torus (Geometry) | Engineering research | Magnetic fields | Mathematical research

Journal Article

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