A note on the structure of prescribed gradient–like domains of non–integrable vector fields
Sign Up to like & getrecommendations! Published in 2021 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.7488
Abstract: Given a geometric structure on ℝn with n=2m (e.g., Euclidean, symplectic, Minkowski, and pseudo‐Euclidean), we analyze the set of points inside the domain of definition of an arbitrary given C1 vector field, where the value… read more here.
Keywords: gradient like; vector field; vector fields; structure ... See more keywords
Global stabilization of switched nonlinear systems with vanishing control vector fields and its application
Sign Up to like & getrecommendations! Published in 2021 at "International Journal of Robust and Nonlinear Control"
DOI: 10.1002/rnc.5534
Abstract: The global stabilization problem for a more extensive class of switched nonlinear systems is studied, in which control vector fields are allowed to vanish at some point, even for all the subsystems at the same… read more here.
Keywords: nonlinear systems; control vector; global stabilization; vector fields ... See more keywords
On scalar and vector fields coupled to the energy-momentum tensor
Sign Up to like & getrecommendations! Published in 2018 at "Journal of High Energy Physics"
DOI: 10.1007/jhep05(2018)100
Abstract: A bstractWe consider theories for scalar and vector fields coupled to the energy-momentum tensor. Since these fields also carry a non-trivial energy-momentum tensor, the coupling prescription generates self-interactions. In analogy with gravity theories, we build… read more here.
Keywords: energy momentum; momentum tensor; vector fields; energy ... See more keywords
On the non-smoothness of the vector fields for the dynamically invariant Beltrami coefficients
Sign Up to like & getrecommendations! Published in 2018 at "Archiv der Mathematik"
DOI: 10.1007/s00013-018-1151-7
Abstract: For $$\mu \in L^{\infty }(\Delta )$$μ∈L∞(Δ), the vector fields on the unit circle determined by $$\mu $$μ play an important role in the theory of the universal Teichmüller space. The aim of this paper is… read more here.
Keywords: vector; non smoothness; dynamically invariant; smoothness vector ... See more keywords
A Global Geometric Decomposition of Vector Fields and Applications to Topological Conjugacy
Sign Up to like & getrecommendations! Published in 2019 at "Acta Applicandae Mathematicae"
DOI: 10.1007/s10440-019-00258-0
Abstract: We give a global geometric decomposition of continuously differentiable vector fields on R n $\mathbb{R}^{n}$ . More precisely, given a vector field of class C 1 $\mathcal{C}^{1}$ on R n $\mathbb{R}^{n}$ , and a geometric… read more here.
Keywords: vector; vector field; vector fields; decomposition ... See more keywords
Primary singularities of vector fields on surfaces
Sign Up to like & getrecommendations! Published in 2018 at "Geometriae Dedicata"
DOI: 10.1007/s10711-019-00497-3
Abstract: Unless another thing is stated one works in the $$C^\infty $$ C ∞ category and manifolds have empty boundary. Let X and Y be vector fields on a manifold M . We say that Y… read more here.
Keywords: vector; primary singularities; primary singularity; fields surfaces ... See more keywords
Structurally Unstable Quadratic Vector Fields of Codimension Two: Families Possessing Either a Cusp Point or Two Finite Saddle-Nodes
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Dynamics and Differential Equations"
DOI: 10.1007/s10884-020-09871-2
Abstract: The goal of this paper is to contribute to the classification of the phase portraits of planar quadratic differential systems according to their structural stability. Artes et al. (Mem Am Math Soc 134:639, 1998) proved… read more here.
Keywords: vector fields; structurally unstable; quadratic vector; phase portraits ... See more keywords
Invariant Algebraic Surfaces of Polynomial Vector Fields in Dimension Three
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Dynamics and Differential Equations"
DOI: 10.1007/s10884-021-10080-8
Abstract: We discuss criteria for the nonexistence, existence and computation of invariant algebraic surfaces for three-dimensional complex polynomial vector fields, thus transferring a classical problem of Poincaré from dimension two to dimension three. Such surfaces are… read more here.
Keywords: vector; algebraic surfaces; polynomial vector; dimension three ... See more keywords
On the Partial Hyperbolicity of Robustly Transitive Sets with Singularities
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Dynamics and Differential Equations"
DOI: 10.1007/s10884-022-10132-7
Abstract: Homoclinic tangencies and singular hyperbolicity are involved in the Palis conjecture for vector fields. Typical three dimensional vector fields are well understood by recent works. We study the dynamics of higher dimensional vector fields that… read more here.
Keywords: robustly transitive; homoclinic tangencies; dimensional vector; vector fields ... See more keywords
Phase Portraits of Random Planar Homogeneous Vector Fields
Sign Up to like & getrecommendations! Published in 2019 at "Qualitative Theory of Dynamical Systems"
DOI: 10.1007/s12346-020-00437-7
Abstract: In this paper, we study the probability of occurrence of phase portraits in the set of random planar homogeneous polynomial vector fields, of degree n . In particular, for $$n=1,2,3,$$ n = 1 , 2… read more here.
Keywords: random planar; planar homogeneous; portraits random; vector fields ... See more keywords
Nonlinear Sliding of Discontinuous Vector Fields and Singular Perturbation
Sign Up to like & getrecommendations! Published in 2018 at "Differential Equations and Dynamical Systems"
DOI: 10.1007/s12591-018-0439-1
Abstract: We consider piecewise smooth vector fields (PSVF) defined in open sets $$M\subseteq \mathbb {R}^n$$M⊆Rn with switching manifold being a smooth surface $$\Sigma $$Σ. We assume that $$M{\setminus }\Sigma $$M\Σ contains exactly two connected regions, namely… read more here.
Keywords: varepsilon; sigma; singular perturbation; regularization ... See more keywords