Title data
Chemnitz, Robin ; Engel, Maximilian ; Koltai, Peter:
Extracting coherent sets in aperiodically driven flows from generators of Mather semigroups.
In: Discrete and Continuous Dynamical Systems. Series B.
(2024)
.
ISSN 15313492
DOI: https://doi.org/10.3934/dcdsb.2024149
This is the latest version of this item.
Abstract in another language
Coherent sets are timedependent regions in the physical space of nonautonomous flows that exhibit little mixing with their neighborhoods, robustly under small random perturbations of the flow. They thus characterize the global longterm transport behavior of the system. We propose a framework to extract such timedependent families of coherent sets for nonautonomous systems with an ergodic driving dynamics and (small) Brownian noise in physical space. Our construction involves the assembly and analysis of an operator on functions over the augmented space of the associated skew product that, for each fixed state of the driving, propagates distributions on the corresponding physicalspace fibre according to the dynamics. This timedependent operator has the structure of a semigroup (it is called the Mather semigroup), and we show that a spectral analysis of its generator allows for a trajectoryfree computation of coherent families, simultaneously for all states of the driving. Additionally, for quasiperiodically driven torus flows, we propose a tailored Fourier discretization scheme for this generator and demonstrate our method by means of three examples of twodimensional flows.
Further data
Item Type:  Article in a journal 

Refereed:  Yes 
Institutions of the University:  Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Dynamical Systems and Data > Chair Dynamical Systems and Data  Univ.Prof. Dr. Peter Koltai Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Dynamical Systems and Data 
Result of work at the UBT:  Yes 
DDC Subjects:  500 Science > 510 Mathematics 
Date Deposited:  23 Oct 2024 08:22 
Last Modified:  23 Oct 2024 08:22 
URI:  https://eref.unibayreuth.de/id/eprint/90824 
Available Versions of this Item

Extracting coherent sets in aperiodically driven flows from generators of Mather semigroups. (deposited 09 Apr 2024 06:46)
 Extracting coherent sets in aperiodically driven flows from generators of Mather semigroups. (deposited 23 Oct 2024 08:22) [Currently Displayed]