arXiv research

Paper classifies transnormal systems on compact 3-manifolds.

The abstract discusses the equivalence of transnormal and isoparametric functions on compact manifolds.

Study on transnormal functions and their level sets on Finsler manifolds.

Among a family of 2-parameter left invariant metrics on Sp(2), we determine which have nonnegative sectional curvatures and which are Einstein. On the quotiente $\widetilde{N}^{11}=(Sp(2)\times S^4)/S^3$, we construct a homogeneous isoparametric foliation with isoparametric hypersurfaces diffeomorphic to Sp(2). Further…

In this note we discuss a few properties of transnormal Finsler functions, i.e., the natural generalization of distance functions and isoparametric Finsler functions. In particular, we prove that critical level sets of an analytic transnormal function are submanifolds, and the partition of $M$ into level sets is a Fins…

The study extends Obata's theorem and classifies Finsler manifolds with transnormal functions.

The paper proves isoparametric functions on Finsler space forms under specific conditions.

The first part of the paper is to improve the fundamental theory of isoparametric functions on general Riemannian manifolds. Next we focus our attention on exotic spheres, especially on "exotic" 4-spheres (if exist) and the Gromoll-Meyer sphere. In particular, as one of main results we prove: there exists no properly t…

Manifold submetries of the round sphere are a class of partitions of the round sphere that generalizes both singular Riemannian foliations, and the orbit decompositions by the orthogonal representations of compact groups. We exhibit a one-to-one correspondence between such manifold submetries and maximal Laplacian alge…

A singular riemannian foliation F on a complete riemannian manifold M is said to admit sections if each regular point of M is contained in a complete totally geodesic immersed submanifold (a section) that meets every leaf of F orthogonally and whose dimension is the codimension of the regular leaves of F. We prove that…

Study on 4-manifolds restricts negatively curved metrics and fundamental groups.

In this paper, we introduce isoparametric functions and isoparametric hypersurfaces in Finsler manifolds and give the necessary and sufficient conditions for a transnormal function to be isoparametric. We then prove that hyperplanes, Minkowski hyperspheres and $F^*$-Minkowski cylinders in a Minkowski space with $BH$-vo…

Given a vector field $X$ in a Riemannian manifold, a hypersurface is said to have a canonical principal direction relative to $X$ if the projection of $X$ onto the tangent space of the hypersurface gives a principal direction. We give different ways for building these hypersurfaces, as well as a number of useful charac…

In this paper we study singular riemannian foliations that have sections,i.e., totally geodesic complete immersed submanifolds that meet each leaf orthogonally and whose dimensions are the codimensions of the regular leaves. We prove here that the restriction of the foliation to a slice of a leaf is diffeomorphic to an…

In this paper, I study the isoparametric hypersurfaces in a Randers sphere $(S^n,F)$ of constant flag curvature, with the navigation datum $(h,W)$. I prove that an isoparametric hypersurface $M$ for the standard round sphere $(S^n,h)$ which is tangent to $W$ remains isoparametric for $(S^n,F)$ after the navigation proc…

Overview of integrable systems with symmetries, focusing on toric and semitoric systems.

New method to derive integrable systems from existing Lax systems.

Learning to control linear systems is statistically hard, especially for underactuated systems.

Discrete-time systems can be characterized by simple flat coordinates and their shifts.

The paper explores when linear system identification is hard or easy, especially for under-actuated systems.

This paper improves system identification by reducing sample complexity for high-dimensional linear dynamical systems.

In integrable hydrodynamic systems, coordinates exist where generators and symmetries are simple.

This paper studies nonholonomic constraints in Hamiltonian systems, deriving equations and theorems.

New method models unknown systems with hidden parameters using neural networks.

Study absolute equivalence for Pfaffian systems, applying to control systems.

Solves selecting the best optimizing system problems.

This paper considers control systems defined on Lie algebroids. After deriving basic controllability tests for general control systems, we specialize our discussion to the class of mechanical control systems on Lie algebroids. This class of systems includes mechanical systems subject to holonomic and nonholonomic const…

Superintegrable systems on curved manifolds found to have Hessian structures.

Systemic risk refers to the risk that the financial system is susceptible to failures due to the characteristics of the system itself. The tremendous cost of systemic risk requires the design and implementation of tools for the efficient macroprudential regulation of financial institutions. The current paper proposes a…

Researchers solve boundary and scattering rigidity problems for magnetic systems.

The paper develops methods to derive mixed superposition rules for Lie systems and applies them to various physical systems.

Paper develops reduction theory for controlled Lagrangian systems with symmetry and momentum map.

The paper studies connections in superintegrable systems, revealing geometric insights.

This paper proposes a system-agnostic policy for dynamic scheduling.

Learn dynamics of a system using auxiliary data from similar systems.

The inability to see and quantify systemic financial risk comes at an immense social cost. Systemic risk in the financial system arises to a large extent as a consequence of the interconnectedness of its institutions, which are linked through networks of different types of financial contracts, such as credit, derivativ…

New Lie systems derived from Goursat distributions with applications to differential equations.

Elliptic systems are characterized by Darboux integrability.

The study analyzes stochastic Lie systems and their applications in various models.

Reduces multisymplectic Lie systems through symmetry analysis.

Study integrable discretizations of cyclic systems with circular coordinate lines.

A new chaotic financial system is proposed by considering ethics involvement in a four-dimensional financial system with market confidence. A five-dimensional conformable derivative financial system is presented by introducing conformable fractional calculus to the integer-order system. A discretization scheme is propo…

A distributed system identification method for LTI systems using reverse experience replay.

This work extends reduction processes for nonholonomic discrete mechanical systems.

Unified approach to deform Lie-Hamilton systems using Poisson-Hopf algebra.

In this paper, we first study the Poisson reductions of controlled Hamiltonian (CH) system and symmetric CH system by controllability distributions. These reductions are the extension of Poisson reductions by distribution for Poisson manifolds to that for phase spaces of CH systems with external force and control. We g…

Maps dBKP solutions to MS system solutions, defining Einstein-Weyl structures.

Proposes a RL method using simulators for stabilizing uncertain systems.