Geodesic
Fixed set theorems for discrete dynamics and nonlinear boundary-value problems
Electronic journal of differential equations, Tome 2011 (2011)
We consider self-mappings of Hausdorff topological spaces which map compact sets to compact sets and establish the existence of invariant (fixed) sets. The fixed set results are used to provide fixed set analogues of well-known fixed point theorems. An algorithm is employed to compute the existence of fixed sets which are self-similar in a generalized sense. Some numerical examples are given. The utility of the abstract result is further illustrated via the study of a boundary value problem for a system of differential equations
Classification : 37B055, 37B10, 37L25, 34B15
Keywords: fixed sets, function system, self-similar sets, invariant sets, Hausdorff metric, Hausdorff topology, boundary value problem 
@article{EJDE_2011__2011__a70,
     author = {Brooks,  Robert and Schmitt,  Klaus and Warner,  Brandon},
     title = {Fixed set theorems for discrete dynamics and nonlinear boundary-value problems},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1246.37033},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a70/}
}
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%A Schmitt,  Klaus
%A Warner,  Brandon
%T Fixed set theorems for discrete dynamics and nonlinear boundary-value problems
%J Electronic journal of differential equations
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%F EJDE_2011__2011__a70
Brooks,  Robert; Schmitt,  Klaus; Warner,  Brandon. Fixed set theorems for discrete dynamics and nonlinear boundary-value problems. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a70/