Fixed point index of area-preserving maps

1975 ◽  
pp. 59-60
Author(s):  
Carl P. Simon
Keyword(s):  
Fixed Point ◽  
Fixed Point Index ◽  
Point Index ◽  
Area Preserving Maps ◽  
Area Preserving

scholarly journals A bound for the fixed point index of area-preserving homeomorphisms of two-manifolds

1987 ◽  
Vol 7 (3) ◽  
pp. 463-479 ◽  
Author(s):  
Stephan Pelikan ◽  
Edward E. Slaminka
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Lebesgue Measure ◽  
Upper Bound ◽  
Fixed Point Index ◽  
Compact Sets ◽  
Point Index ◽  
Area Preserving Maps ◽  
Area Preserving

AbstractThe study of area preserving maps of manifolds has an extensive history in the theory of dynamical systems. One interest has been in the behaviour of such maps near an isolated fixed point. In 1974 Carl Simon proved the existence of an upper bound for the index of an isolated fixed point for Ck area preserving diffeomorphisms of a surface. We extend his result to homeomorphisms of an orientable two manifold. The proof utilizes the notion of free modification, developed by Morton Brown, and enlarges the scope of the problem to the consideration of ‘nice’ measures, i.e. uniformly equivalent to Lebesgue measure on compact sets. By suitably modifying the homeomorphism and the measure, we obtain the following theorem.

scholarly journals Nontrivial Solutions of Systems of Perturbed Hammerstein Integral Equations with Functional Terms

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 330
Author(s):  
Gennaro Infante
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Integral Equations ◽  
General Class ◽  
Fixed Point Index ◽  
Nontrivial Solutions ◽  
Point Index ◽  
Hammerstein Integral Equations ◽  
Functional Boundary ◽  
Functional Boundary Conditions

We discuss the solvability of a fairly general class of systems of perturbed Hammerstein integral equations with functional terms that depend on several parameters. The nonlinearities and the functionals are allowed to depend on the components of the system and their derivatives. The results are applicable to systems of nonlocal second order ordinary differential equations subject to functional boundary conditions, this is illustrated in an example. Our approach is based on the classical fixed point index.

A fixed point index for maps with Borsuk-presentable fixed point set

1982 ◽  
Vol 38 (1) ◽  
pp. 549-555
Author(s):  
Christian C. Fenske
Keyword(s):  
Fixed Point ◽  
Fixed Point Index ◽  
Point Index ◽  
Fixed Point Set ◽  
Point Set

scholarly journals Fixed point index and decompositions of isolated invariant compacta

2004 ◽  
Vol 141 (1-3) ◽  
pp. 207-223
Author(s):  
Francisco R. Ruiz del Portal ◽  
José M. Salazar
Keyword(s):  
Fixed Point ◽  
Fixed Point Index ◽  
Point Index
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