Book ChapterDOI
Mesure de Lebesgue et Nombre de Rotation
Michael Robert Herman
- pp 271-293
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The article was published on 1977-01-01. It has received 120 citations till now.read more
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Methods of qualitative theory in nonlinear dynamics
TL;DR: In this paper, the behavior of dynamical systems on the stability boundary of equilibria is investigated on the route over stability boundary, at the disappearance of a saddle-node equilibrium state, and on the trajectory of periodic trajectories.
Journal ArticleDOI
Bifurcations and stability of families of diffeomorphisms
TL;DR: In this article, the first bifurcation point of a diffeomorphism is characterized, and a model for the local unfoldings of the periodic orbits of the diffeomorphic arcs is established.
Journal ArticleDOI
Phase locking, period doubling bifurcations and chaos in a mathematical model of a periodically driven oscillator: a theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmias.
Michael R. Guevara,Leon Glass +1 more
TL;DR: It is proposed that cardiac dysrhythmias may arise from desynchronization of two or more spontaneously oscillating regions of the heart and serve to account for the various forms of atrioventricular (AV) block clinically observed.
Journal ArticleDOI
Chaotic behavior in piecewise continuous difference equations
TL;DR: A class of piecewise continuous mappings with positive slope, mapping the unit interval into itself is studied in this article, where the asymptotic behavior depends sensitively on initial data in that the rotation number is either a nowhere continuous function of initial data, or else it is a constant on all but a Cantor set of the unit intervals.