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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.

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
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