Naslov
Linearization for difference equations with infinite delay

Autori
Singh, Lokesh

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Book of Abstracts, 7th Croatian Mathematical Congress / Ćurković, Andrijana ; Grbac, Zorana ; Jadrijević, Borka ; Klaričić Bakula, Milic - Split : Prirodoslovno-matematički fakultet Sveučilišta u Splitu, 2022, 73-73

Skup
7th Croatian Mathematical Congress

Mjesto i datum
Split, Hrvatska, 15.06.2022. - 18.06.2022

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
difference equations: infinite delay ; linearization

Sažetak
One of the most common technique to study a nonlinear dynamics is to find an equivalent linear dynamics. The process of constructing a map, which transforms a nonlinear dynamics into a linear dynamics is commonly known as Linearization. Let ( X , ∥ ⋅ ∥ ) be an arbitrary Banach space and let B := {; ϕ : Z − → X ∣ ∣ ∥ ϕ ∥ B < ∞ }; be a Banach space of sequences with appropriate norm ∥ ⋅ ∥ B . Given m ∈ Z + and a sequence x : Z → X , define a new sequence x m : Z − → X given by x m ( j ) := x ( m + j ) for all j ∈ Z − . In this talk, I am going to present a result on the Linearization of Difference equation with infinite delay, x ( m + 1 ) = A m x m + f m ( x m ) for all m ∈ Z + , (1) in a Banach Space X . Here we assume that for each m ∈ Z + , A m : B → X is a bounded linear map and the perturbation ( f m ) m ∈ Z + is small and Lipschitz. In this result, a sequence of continuous and one-one maps, ( h m ) m ∈ Z + , is constructed which gives equivalency between the nonlinear dynamics (1) and its linear counterpart. We also showed that when ( A m ) m ∈ Z + admits exponential dichotomy, our result is applicable.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA