About: Markus–Yamabe conjecture

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In mathematics, the Markus–Yamabe conjecture is a conjecture on global asymptotic stability. If the Jacobian matrix of a dynamical system at a fixed point is Hurwitz, then the fixed point is asymptotically stable. Markus-Yamabe conjecture asks if a similar result holds globally. Precisely, the conjecture states that if a continuously differentiable map on an -dimensional real vector space has a fixed point, and its Jacobian matrix is everywhere Hurwitz, then the fixed point is globally stable.

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rdf:type	yago:WikicatConjectures yago:WikicatTheoremsInDynamicalSystems yago:Abstraction100002137 yago:Cognition100023271 yago:Communication100033020 yago:Concept105835747 yago:Content105809192 yago:Hypothesis105888929 yago:Idea105833840 yago:Message106598915 yago:Proposition106750804 yago:PsychologicalFeature100023100 yago:Speculation105891783 yago:Statement106722453 yago:Theorem106752293
rdfs:label	Conjetura de Markus–Yamabe (es) Markus–Yamabe conjecture (en)
rdfs:comment	En matemáticas, la conjetura de Markus–Yamabe es una conjetura sobre la estabilidad asintótica global. La conjetura dice que si un mapa continuamente diferenciable en un espacio vectorial real de dimensión tiene un punto fijo, y su jacobiana es siempre una matriz de Hurwitz, entonces el punto fijo es globalmente estable. La conjetura es verdadera para los casos bidimensionales. Sin embargo, se han creado contraejemplos en dimensiones superiores. Por lo tanto, sólo en el caso bidimensional, también se puede referir al teorema de Markus–Yamabe. (es) In mathematics, the Markus–Yamabe conjecture is a conjecture on global asymptotic stability. If the Jacobian matrix of a dynamical system at a fixed point is Hurwitz, then the fixed point is asymptotically stable. Markus-Yamabe conjecture asks if a similar result holds globally. Precisely, the conjecture states that if a continuously differentiable map on an -dimensional real vector space has a fixed point, and its Jacobian matrix is everywhere Hurwitz, then the fixed point is globally stable. (en)
dcterms:subject	Fixed points (mathematics) Disproved conjectures Theorems in dynamical systems Stability theory
Wikipage page ID	7726067 (xsd:integer)
Wikipage revision ID	1109436789 (xsd:integer)
Link from a Wikipage to another Wikipage	Fixed points (mathematics) Vector space Mathematics Conjecture Smooth function Disproved conjectures Fixed point (mathematics) Kalman's conjecture Jacobian matrix Jacobian matrix and determinant Hurwitz matrix Asymptotic stability Advances in Mathematics Theorems in dynamical systems Autonomous convergence theorem Stability theory Real number
Link from a Wikipage to an external page	http://www.worldscientific.com/doi/pdf/10.1142/S0218127413300024 http://www.math.spbu.ru/user/nk/PDF/2011-TiSU-Hidden-oscillations-attractors-Aizerman-Kalamn-conjectures.pdf https://dx.doi.org/10.1134/S106423071104006X https://dx.doi.org/10.1142/S0218127413300024 https://projecteuclid.org/euclid.ojm/1200689999 http://www.math.unl.edu/~gmeisters1/papers/HK1996.pdf
sameAs	Markus–Yamabe conjecture Markus–Yamabe conjecture Markus–Yamabe conjecture Markus–Yamabe conjecture
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bot	InternetArchiveBot (en)
date	June 2017 (en)
fix-attempted	yes (en)
has abstract	En matemáticas, la conjetura de Markus–Yamabe es una conjetura sobre la estabilidad asintótica global. La conjetura dice que si un mapa continuamente diferenciable en un espacio vectorial real de dimensión tiene un punto fijo, y su jacobiana es siempre una matriz de Hurwitz, entonces el punto fijo es globalmente estable. La conjetura es verdadera para los casos bidimensionales. Sin embargo, se han creado contraejemplos en dimensiones superiores. Por lo tanto, sólo en el caso bidimensional, también se puede referir al teorema de Markus–Yamabe. Resultados matemáticos relacionados con la estabilidad asintótica global, los cuales son aplicables en dimensiones superiores a dos, incluyen varios teoremas de convergencia autónoma. Análogas de la conjetura para sistemas de control no lineales con no linealidad escalar son conocidas como conjeturas de Kalman. (es) In mathematics, the Markus–Yamabe conjecture is a conjecture on global asymptotic stability. If the Jacobian matrix of a dynamical system at a fixed point is Hurwitz, then the fixed point is asymptotically stable. Markus-Yamabe conjecture asks if a similar result holds globally. Precisely, the conjecture states that if a continuously differentiable map on an -dimensional real vector space has a fixed point, and its Jacobian matrix is everywhere Hurwitz, then the fixed point is globally stable. The conjecture is true for the two-dimensional case. However, counterexamples have been constructed in higher dimensions. Hence, in the two-dimensional case only, it can also be referred to as the Markus–Yamabe theorem. Related mathematical results concerning global asymptotic stability, which are applicable in dimensions higher than two, include various autonomous convergence theorems. Analog of the conjecture for nonlinear control system with scalar nonlinearity is known as Kalman's conjecture. (en)
prov:wasDerivedFrom	wikipedia-en:Markus–Yamabe_conjecture?oldid=1109436789&ns=0
page length (characters) of wiki page	3738 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Markus–Yamabe_conjecture
is Link from a Wikipage to another Wikipage of	Kalman's conjecture Autonomous convergence theorem Lyapunov stability Markus-Yamabe Conjecture Markus-Yamabe conjecture Yamabe conjecture Markus-Yamabe Theorem Markus−Yamabe conjecture Markus−Yamabe theorem
is Wikipage redirect of	Markus-Yamabe Conjecture Markus-Yamabe conjecture Yamabe conjecture Markus-Yamabe Theorem Markus−Yamabe conjecture Markus−Yamabe theorem
is foaf:primaryTopic of	wikipedia-en:Markus–Yamabe_conjecture

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