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On the solution of the 33rd Palis-Pugh problem for gradient-like diffeomorphisms of a 2-sphere. (English. Russian original) Zbl 1447.37029
Russ. Math. Surv. 75, No. 2, 383-385 (2020); translation from Usp. Mat. Nauk 75, No. 2, 195-196 (2020).
From the text: The problem of the existence of an arc with an at most countable (a finite) number of bifurcations and connecting structurally stable systems (Morse-Smale systems) on manifolds was number 33 in the list of 50 Palis-Pugh problems [J. Palis and C. Pugh, Fifty problems on dynamical systems, Lect. Notes Math. 468, 345-353 (1975; Zbl 0304.58011)]. In this note we outline a solution to this problem for gradient-like diffeomorphisms of a two-dimensional sphere.
MSC:
37C05 Dynamical systems involving smooth mappings and diffeomorphisms
37C20 Generic properties, structural stability of dynamical systems
37B35 Gradient-like and recurrent behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems
37D15 Morse-Smale systems
37G10 Bifurcations of singular points in dynamical systems
37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
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