scholarly journals Contraction Theory for Dynamical Systems on Hilbert Spaces

2021 ◽  
pp. 1-1
Author(s):  
Pedro Cisneros-Velarde ◽  
Saber Jafarpour ◽  
Francesco Bullo
Keyword(s):  
Dynamical Systems ◽  
Hilbert Spaces ◽  
Contraction Theory

scholarly journals Nonpivot and Implicit Projected Dynamical Systems on Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Monica Gabriela Cojocaru ◽  
Stephane Pia
Keyword(s):  
Dynamical Systems ◽  
Variational Inequalities ◽  
Hilbert Spaces ◽  
Dual Space ◽  
Variational Problems ◽  
Base Space ◽  
Projected Dynamical Systems

This paper presents a generalization of the concept and uses of projected dynamical systems to the case of nonpivot Hilbert spaces. These are Hilbert spaces in which the topological dual space is not identified with the base space. The generalization consists of showing the existence of such systems and their relation to variational problems, such as variational inequalities. In the case of usual Hilbert spaces these systems have been extensively studied, and, as in previous works, this new generalization has been motivated by applications, as shown below.

Rigged Hilbert spaces for chaotic dynamical systems

1996 ◽  
Vol 37 (11) ◽  
pp. 5837-5847 ◽  
Author(s):  
Z. Suchanecki ◽  
I. Antoniou ◽  
S. Tasaki ◽  
O. F. Bandtlow
Keyword(s):  
Dynamical Systems ◽  
Hilbert Spaces ◽  
Rigged Hilbert Spaces ◽  
Chaotic Dynamical Systems

scholarly journals Almost periodicity and periodicity for nonautonomous random dynamical systems

2020 ◽  
pp. 2150034
Author(s):  
Paul Raynaud de Fitte
Keyword(s):  
Partial Differential Equations ◽  
Dynamical Systems ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Random Processes ◽  
Random Dynamical Systems ◽  
Almost Periodicity ◽  
Almost Periodic

We present a notion of almost periodicity which can be applied to random dynamical systems as well as almost periodic stochastic differential equations in Hilbert spaces (abstract stochastic partial differential equations). This concept allows for improvements of known results of almost periodicity in distribution, for general random processes and for solutions to stochastic differential equations.

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