Let f be a smooth self-map of R m , when m is an arbitrary natural number. We give a complete description of possible sequences of indices of iterations of f at an isolated fixed point, answering in affirmative the Chow, Mallet-Paret and Yorke conjecture posed in [S.N. Chow, J. Mallet-Parret, J.A. Yorke, A periodic point index which is a bifurcation invariant, in: Geometric Dynamics, Rio de Janeiro,
Let f be a local planar homeomorphism with an isolated fixed point at 0. We study the form of the sequence {ind(f n , 0)} n =0 , where ind(f, 0) is a fixed point index at 0.
Abstract. We construct a degree-type otopy invariant for equivariant gradient local maps in the case of a real finite-dimensional orthogonal representation of a compact Lie group. We prove that the invariant establishes a bijection between the set of equivariant gradient otopy classes and the direct sum of countably many copies of Z.Mathematics Subject Classification. Primary 55P91; Secondary 54C35.
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