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Applications of Covering Map**s in the Theory of Implicit Differential Equations
This paper is a brief review of results in the theory of covering map**s of metric spaces and vector metric spaces and its applications to implicit...
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Free Cyclic Actions on Surfaces and the Borsuk—Ulam Theorem
Let M and N be topological spaces, let G be a group, and let τ : G × M → M be a proper free action of G . In this paper, we define a Borsuk—Ulam-type...
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Nielsen coincidence theory on infra-solvmanifolds of Sol
We derive averaging formulas for the Lefschetz coincidence numbers, the Nielsen coincidence numbers and the Reidemeister coincidence numbers of maps...
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Colorful Coverings of Polytopes and Piercing Numbers of Colorful d-Intervals
We prove a common strengthening of Bárány’s colorful Carathéodory theorem and the KKMS theorem. In fact, our main result is a colorful polytopal KKMS...
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A forcing relation of braids from Nielsen fixed point theory
Abstract In this paper, we focus our attention on the connections between the braid group and Nielsen fixed point theory. A new forcing relation...
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Difference cochains and Reidemeister traces
The authors consider the difference of Reidemeister traces and difference cochain of given two self-maps, and find out a relation involving these two...
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Some developments in Nielsen fixed point theory
We give a brief survey of some developments in Nielsen fixed point theory. After a look at early history and a digress to various generalizations, we...
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Self-maps of S 2 homotopic to a smooth map with a single n-periodic point
We show for which ( d , n ) ∈ ℤ × ℕ there exists a smooth self-map f : S 2 → S 2 so that deg( f ) = d and Fix( f n ) is a point.
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When a smooth self-map of a semi-simple Lie group can realize the least number of periodic points
There are two algebraic lower bounds of the number of n -periodic points of a self-map f : M → M of a compact smooth manifold of dimension at least 3: NF ...
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Bolzano’s theorems for holomorphic map**s
The existence of a zero for a holomorphic functions on a ball or on a rectangle under some sign conditions on the boundary generalizing Bolzano’s...
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Fixed points of n-valued maps on surfaces and the Wecken property—a configuration space approach
In this paper, we explore the fixed point theory of n -valued maps using configuration spaces and braid groups, focusing on two fundamental problems,...
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Cube-like complexes, Steinhaus’ chains and the Poincaré–Miranda theorem
We discuss combinatorial results allowing to prove a new, more general version of the Poincaré–Miranda fixed point theorem. The main tool is the...
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Coincidence invariants and higher Reidemeister traces
The Lefschetz number and fixed point index can be thought of as two different descriptions of the same invariant. The Lefschetz number is algebraic...
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Uniqueness of dynamical zeta functions and symmetric products
A characterization of dynamically defined zeta functions is presented. It comprises a list of axioms, natural extension of the one which...