Bogatyi, S. A.; Skordev, G. S. A coincidence theorem for \(M\)-like continua. (English. Russian original) Zbl 1042.37010 Russ. Math. Surv. 57, No. 2, 410-412 (2002); translation from Usp. Mat. Nauk 57, No. 2, 189-190 (2002). Introduction: In the investigation of the dynamical properties of a rational (or even a polynomial) map \(f:S^2\to S^2\) of the Riemann sphere into itself it is helpful to consider the lamination \((S^2,f)\). We study properties of the lamination that are close to fixed-point properties. Here, we consider laminations obtained from ‘variable’ maps of a fixed compact connected oriented manifold \(M^n\) without boundary. Cited in 1 Document MSC: 37B45 Continua theory in dynamics 37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics 37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets 54F15 Continua and generalizations 55M20 Fixed points and coincidences in algebraic topology 37E99 Low-dimensional dynamical systems Keywords:maps of manifolds; lamination; fixed-point properties PDFBibTeX XMLCite \textit{S. A. Bogatyi} and \textit{G. S. Skordev}, Russ. Math. Surv. 57, No. 2, 410--412 (2002; Zbl 1042.37010); translation from Usp. Mat. Nauk 57, No. 2, 189--190 (2002) Full Text: DOI