scholarly journals Lefschetz fixed point theorem for acyclic maps with multiplicity

2002 ◽  
Vol 19 (2) ◽  
pp. 339 ◽  
Author(s):  
Fritz Von Haeseler ◽  
Heinz-Otto Peitgen ◽  
Gencho Skordev
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Lefschetz Fixed Point Theorem

ON SOME NONAUTONOMOUS CHAOTIC SYSTEM ON THE PLANE

1999 ◽  
Vol 09 (09) ◽  
pp. 1853-1858 ◽  
Author(s):  
KLAUDIUSZ WÓJCIK
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Fixed Point Theorem ◽  
Chaotic System ◽  
Point Theorem ◽  
Chaotic Behavior ◽  
Topological Methods ◽  
Lefschetz Fixed Point Theorem ◽  
Nonautonomous Equations ◽  
Time Periodic

We prove the existence of the chaotic behavior in dynamical systems generated by some class of time periodic nonautonomous equations on the plane. We use topological methods based on the Lefschetz Fixed Point Theorem and the Ważewski Retract Theorem.

On the Homotopy Property of Nussbaum's Fixed Point Index

1982 ◽  
Vol 34 (1) ◽  
pp. 44-62
Author(s):  
Gilles Fournier ◽  
Reine Fournier
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Index ◽  
Point Index ◽  
Homotopy Property ◽  
Lefschetz Fixed Point Theorem ◽  
The One ◽  
Compact Map ◽  
General Conditions

In [14] R. D. Nussbaum generalized the fixed point index to a class of maps larger than the one in [5]. Unfortunately his homotopy property conditions are more restrictive than the often more readily verifiable ones of Eells-Fournier. In this paper we shall try to find an intermediate class of maps which will contain all the known examples of maps for which the index is defined and for which the condition of Eells-Fournier will imply the homotopy property.In doing so, we shall give general conditions for which the sum of a compact map and a differentiable map will be a map having a fixed point index and for which the Lefschetz fixed point theorem is true.

Sign in / Sign up

Export Citation Format

Share Document