TY - JOUR

T1 - Multiscale Conditional Shadowing

AU - Pilyugin, Sergei Yu

N1 - Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2024

Y1 - 2024

N2 - In this paper, we study conditional shadowing for a nonautonomous system in a Banach space assuming that the linear part admits a family of invariant subspaces (scale) with different behavior of trajectories. Conditions of shadowing are formulated in terms of smallness of the projections of one-step errors to the scale and of smallness of Lipschitz constants of the projections of nonlinear terms. We also give conditions under which a system has the conditional property of inverse shadowing (dual to the shadowing property).

AB - In this paper, we study conditional shadowing for a nonautonomous system in a Banach space assuming that the linear part admits a family of invariant subspaces (scale) with different behavior of trajectories. Conditions of shadowing are formulated in terms of smallness of the projections of one-step errors to the scale and of smallness of Lipschitz constants of the projections of nonlinear terms. We also give conditions under which a system has the conditional property of inverse shadowing (dual to the shadowing property).

KW - Dynamical system

KW - Hyperbolicity

KW - Inverse shadowing

KW - Shadowing

UR - http://www.scopus.com/inward/record.url?scp=85118327554&partnerID=8YFLogxK

U2 - 10.1007/s10884-021-10096-0

DO - 10.1007/s10884-021-10096-0

M3 - Article

AN - SCOPUS:85118327554

VL - 36

SP - 323

EP - 332

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

SN - 1040-7294

IS - Issue Suppl 1

ER -