scholarly journals Nonuniform dichotomy spectrum and reducibility for nonautonomous equations

2015 ◽  
Vol 139 (5) ◽  
pp. 538-557 ◽  
Author(s):  
Jifeng Chu ◽  
Fang-Fang Liao ◽  
Stefan Siegmund ◽  
Yonghui Xia ◽  
Weinian Zhang
Keyword(s):  
Dichotomy Spectrum ◽  
Nonautonomous Equations

scholarly journals Reduction principle at work

2021 ◽  
Vol 8 (1) ◽  
pp. 46-74
Author(s):  
Christian Pötzsche ◽  
Evamaria Russ
Keyword(s):  
Center Manifold ◽  
Reduction Principle ◽  
Critical Stability ◽  
Center Manifold Reduction ◽  
Infinite Dimensional ◽  
Linearized Stability ◽  
Dichotomy Spectrum ◽  
Nonautonomous Case ◽  
Necessary And Sufficient ◽  
Manifold Reduction

Abstract The purpose of this informal paper is three-fold: First, filling a gap in the literature, we provide a (necessary and sufficient) principle of linearized stability for nonautonomous difference equations in Banach spaces based on the dichotomy spectrum. Second, complementing the above, we survey and exemplify an ambient nonautonomous and infinite-dimensional center manifold reduction, that is Pliss’s reduction principle suitable for critical stability situations. Third, these results are applied to integrodifference equations of Hammerstein- and Urysohn-type both in C- and Lp -spaces. Specific features of the nonautonomous case are underlined. Yet, for the simpler situation of periodic time-dependence even explicit computations are feasible.

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.

scholarly journals NONUNIFORM DICHOTOMY SPECTRUM INTERVALS: THEOREM AND COMPUTATION

2019 ◽  
Vol 9 (3) ◽  
pp. 1102-1119
Author(s):  
Hailong Zhu ◽  
◽  
Zhaoxiang Li ◽  
◽  
Keyword(s):  
Dichotomy Spectrum
Sign in / Sign up

Export Citation Format

Share Document