arXiv research

Metrics are isometric for certain Anosov magnetic systems.

The paper explores how magnetic systems' spectra can identify metrics and 1-forms.

Anosov magnetic flows on surfaces are characterized.

Study magnetic potentials on Anosov manifolds using spectral data.

Assume (M,g,Ω) is a closed, oriented Riemannian surface equipped with an Anosov magnetic flow. We establish certain results on the surjectivity of the adjoint of the magnetic ray transform, and use these to prove the injectivity of the magnetic ray transform on sums of tensors of degree at most two. In the final sectio…

Guillarmou extends X-ray transform to magnetic and thermostat flows.

Smooth orbit equivalence proves metric equivalence for geodesic flows.

We consider a magnetic flow without conjugate points on a closed manifold $M$ with generating vector field $\G$. Let $h\in C^{\infty}(M)$ and let $θ$ be a smooth 1-form on $M$. We show that the cohomological equation \[\G(u)=h\circ π+θ\] has a solution $u\in C^{\infty}(SM)$ only if $h=0$ and $θ$ is closed. This result …

Extends E. Hopf's theorem to magnetic systems without conjugate points.

This paper studies Hamilton-Jacobi equations for magnetic systems with constraints.

We consider an optical hypersurface $Σ$ in the cotangent bundle $τ:T^*M\to M$ of a closed manifold $M$ endowed with a twisted symplectic structure. We show that if the characteristic foliation of $Σ$ is Anosov, then a smooth 1-form $θ$ on $M$ is exact if and only $τ^*θ$ has zero integral over every closed characteristi…

In this paper we study rigidity aspects of Zoll magnetic systems on closed surfaces. We characterize magnetic systems on surfaces of positive genus given by constant curvature metrics and constant magnetic functions as the only magnetic systems such that the associated Hamiltonian flow is Zoll, i.e. every orbit is clos…

Study shows finiteness of magnetic hypersurfaces on closed manifolds.

Researchers prove integrability of magnetic systems on spheres up to dimension 6.

New findings on magnetic geodesic flows and periodic motions.

Study magnetic curvature on Lie groups, extending Milnor's work.

The paper defines a critical value for a magnetic system and extends solutions beyond blow-up.

Study magnetic Hamiltonian systems with constraints, deriving Hamilton-Jacobi equations.

Study reveals new geometric structures for magnetic field Hamiltonian systems.

Researchers solve boundary and scattering rigidity problems for magnetic systems.

Combines geometric hydrodynamics with magnetic systems to derive new equations and prove well-posedness.

Study magnetic geodesics on odd spheres, computing critical energy values.

The article finds non-trivial Zoll magnetic systems for surfaces of any genus.

Global singularities propagate in magnetic mechanical systems on Riemannian manifolds.

Study of gyroscopic Chaplygin systems and magnetic flows on spheres.

Challenge to separate Earth's magnetic field from vehicle's magnetic field for accurate navigation.

A controlled magnetic Hamiltonian (CMH) system is a regular controlled Hamiltonian (RCH) system with magnetic symplectic form, it is an important special case of RCH system. Note that there is a magnetic term on the cotangent bundle of the Heisenberg group, such that we can define a CMH system with symmetry of the Heis…

Constructs smooth integrable magnetic systems on a two-torus.

Study rigidity of Hamiltonians near a minimum in symplectic and magnetic settings.

Normal forms prove dynamical results for magnetic fields on surfaces.

Examples are presented of how the geometric notion of the mean curvature is used for general magnetic field configurations and magnetic surfaces. It is shown that the mean magnetic curvature is related to the variation of the absolute value of the magnetic field along its lines. Magnetic surfaces of constant mean curva…

New tree structure for pseudo-Anosovs from interval maps.

MagNet uses neural networks to predict multi-agent dynamics from observations.

Study on magnetic field and potential systems to prove rigidity results.

Let $M$ be a closed oriented surface and let $Ω$ be a non-exact 2-form. Suppose that the magnetic flow $φ$ of the pair $(g,Ω)$ is Anosov. We show that the longitudinal KAM-cocycle of $φ$ is a coboundary if and only the Gaussian curvature is constant and $Ω$ is a constant multiple of the area form thus extending the res…

Paper studies non-associativity in quantum systems with magnetic fields.

The paper studies magnetic geodesic flows on 2-surfaces with integrable structures.

Study magnetic geodesics on half-Lie groups, proving Hopf-Rinow theorem for energies above critical value.

Study magnetic field evolution in inhomogeneous axion stars.

The paper studies stability of discretized Anosov flows.

Study isotropic embeddings of Lie group orbits and their application to magnetic geodesic flows.

Anosov flow found in specific partially hyperbolic systems.

We consider magnetic geodesic flows of the normal metrics on a class of homogeneous spaces, in particular (co)adjoint orbits of compact Lie groups. We give the proof of the non-commutative integrability of flows and show, in addition, for the case of (co)adjoint orbits, the usual Liouville integrability by means of ana…

For a two-dimensional simple magnetic system, we study the attenuated magnetic ray transform $I_{A,Φ}$, with attenuation given by a unitary connection $A$ and a skew-Hermitian Higgs field $Φ$. We give a description for the range of $I_{A,Φ}$ acting on $\mathbb C^n$-valued tensor fields.

In this paper, we consider a compact Riemannian manifold with boundary, endowed with a magnetic potential $α$ and a potential $U$. For brevity, this type of systems are called $\MP$-systems. On simple $\MP$-systems, we consider both the boundary rigidity problem and scattering rigidity problem, see the introduction for…

Integrates magnetic geodesic and sub-Riemannian flows on Stefel variety, proving integrability and Lax presentations.

We prove a generalization of Livsic's Theorem on the vanishing of the cohomology of certain types of dynamical systems. As a consequence, we strengthen a result due to Zimmer concerning algebraic hulls of Anosov actions of semisimple Lie groups. Combining this with Topological Superrigidity, we find a Holder geometric …

We consider a periodic problem for the motion of a charged particle in a magnetic field. Introducing a notion of Ricci curvature for such Lagrangian systems and using the methods of the calculus of variations in the large, we prove the existence of periodic motions for such particles under a condition of positivity of …