PERIODICITY AND SHARKOVSKY'S THEOREM FOR RANDOM DYNAMICAL SYSTEMS

2001 ◽  
Vol 01 (03) ◽  
pp. 299-338 ◽  
Author(s):  
MARC KLÜNGER
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Fixed Point Theorem ◽  
Periodic Orbits ◽  
Point Theorem ◽  
Random Dynamical Systems ◽  
Random Fixed Point ◽  
One Dimensional ◽  
Sharkovsky's Theorem ◽  
Random Fixed Point Theorem

We generalize the deterministic notion of periodicity to random dynamical systems, which leads to three different objects, called random periodic orbits, point and cycles. We analyze the relation of these three notions and prove a "random fixed point theorem" for one-dimensional random dynamical systems. Finally we use these notions to prove partial generalizations of Sharkovsky's theorem to random dynamical systems.

Existence results for a class of random delay integrodifferential equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Amadou Diop ◽  
Mamadou Abdul Diop ◽  
K. Ezzinbi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Operator Theory ◽  
Mild Solutions ◽  
Random Delay ◽  
Random Fixed Point ◽  
Unbounded Delay ◽  
Carathéodory Conditions ◽  
Random Fixed Point Theorem

Abstract In this paper, we consider a class of random partial integro-differential equations with unbounded delay. Existence of mild solutions are investigated by using a random fixed point theorem with a stochastic domain combined with Schauder’s fixed point theorem and Grimmer’s resolvent operator theory. The results are obtained under Carathéodory conditions. Finally, an example is provided to illustrate our results.

scholarly journals An Application of Random Fixed Point Theorem in Integral Equation

2014 ◽  
Vol 9 (4) ◽  
pp. 57-61
Author(s):  
Mukti Gangopadhyay ◽  
◽  
Pritha Dan ◽  
M. Saha
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Random Fixed Point ◽  
Random Fixed Point Theorem
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