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
On Topological Classification of Gradient-like Flows on an $$n$$ -sphere in the Sense of Topological Conjugacy
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DOI: 10.1134/s1560354720060143
Abstract: In this paper, we study gradient-like flows without heteroclinic intersections on an $$n$$ -sphere up to topological conjugacy. We prove that such a flow is completely defined by a bicolor tree corresponding to a skeleton… read more here.
Keywords: like flows; topological classification; topological conjugacy; gradient ... See more keywords
Scenario of stable transition from diffeomorphism of torus isotopic to identity one to skew product of rough transformations of circle
Sign Up to like & getrecommendations! Published in 2024 at "Ufa Mathematical Journal"
DOI: 10.13108/2024-16-1-10
Abstract: In this paper, we consider gradient-like diffeomorphisms of a two-dimensional torus isotopic to the identical one. The isotopicity of diffeomorphisms $f_0$, $f_1$ on an $n$-manifold $M^n$ means the existence of some arc $\{f_t:M^n\to M^n,t\in[0,1]\}$ connecting… read more here.
Keywords: torus isotopic; diffeomorphism; torus; rough transformations ... See more keywords