Injectivity and almost global asymptotic stability of Hurwitz vector fields

Castañeda, Álvaro; Guíñez, Víctor

doi:10.1016/j.jmaa.2016.12.078

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Injectivity1

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Cited by 3 publications

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“…Remark 2. The Proposition 3 in dimension three is Theorem 2.2 from [2]. Additionally, in the same article, in Remark 2.4 we give the inverse of F on explicitly way but without details as was constructed.…”

Section: Injectivitymentioning

confidence: 99%

Nilpotent Jacobians and Almost Global Stability

Castañeda¹,

Higuera²

2018

Preprint

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In this article we study maps with nilpotent Jacobian in R n distinguishing the cases when the rows of JH are linearly dependent over R and when they are linearly independent over R. In the linearly dependent case, we show an application of such maps on dynamical systems, in particular, we construct a large family of almost Hurwitz vector fields for which the origin is an almost global attractor. In the linearly independent case, we show explicitly the inverse maps of the counterexamples to Generalized Dependence Problem and proving that this inverse maps also have nilpotent Jacobian with rows linearly independent over R.

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Section: Injectivitymentioning

confidence: 99%