Displaying similar documents to “Some Recent Rigorous Results in the Theory of Phase Transitions and Critical Phenomena”

A polynomial with 2k critical values at infinity

Janusz Gwoździewicz, Maciej Sękalski (2004)

Annales Polonici Mathematici

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We construct a polynomial f:ℂ² → ℂ of degree 4k+2 with no critical points in ℂ² and with 2k critical values at infinity.

Chordal cubic systems.

Marc Carbonell, Jaume Llibre (1989)

Publicacions Matemàtiques

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We classify the phase portraits of the cubic systems in the plane such that they do not have finite critical points, and the critical points on the equator of the Poincaré sphere are isolated and have linear part non-identically zero.

Density of Critical Factorizations

Tero Harju, Dirk Nowotka (2010)

RAIRO - Theoretical Informatics and Applications

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We investigate the density of critical factorizations of infinite sequences of words. The density of critical factorizations of a word is the ratio between the number of positions that permit a critical factorization, and the number of all positions of a word. We give a short proof of the Critical Factorization Theorem and show that the maximal number of noncritical positions of a word between two critical ones is less than the period of that word. Therefore, we consider only...