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Intro to Nonautonomous Dynamical Systems & Their Attractor

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Intro to Nonautonomous Dynamical Systems & Their AttractorThe nature of time in a nonautonomous dynamical system is very different from that in autonomous systems, which depend only on the time that has elapsed since starting rather than on the actual time itself. Consequently, limiting objects may not exist in actual time as in autonomous systems. New concepts of attractors in nonautonomous dynamical system are thus required. In addition, the definition of a dynamical system itself needs to be generalised

The nature of time in a nonautonomous dynamical system is very different from that in autonomous systems, which depend only on the time that has elapsed since starting rather than on the actual time itself. Consequently, limiting objects may not exist in actual time as in autonomous systems. New concepts of attractors in nonautonomous dynamical system are thus required.

In addition, the definition of a dynamical system itself needs to be generalised to the nonautonomous context. Here two possibilities are considered: two-parameter semigroups or processes and the skew product flows. Their attractors are defined in terms of families of sets that are mapped onto each other under the dynamics rather than a single set as in autonomous systems. Two types of attraction are now possible: pullback attraction, which depends on the behaviour from the system in the distant past, and forward attraction, which depends on the behaviour of the system in the distant future. These are generally independent of each other.

The component subsets of pullback and forward attractors exist in actual time. The asymptotic behaviour in the future limit is characterised by omega-limit sets, in terms of which form what are called forward attracting sets. They are generally not invariant in the conventional sense, but are asymptotically invariant in general and, if the future dynamics is appropriately uniform, also asymptotically negatively invariant.

Much of this book is based on lectures given by the authors in Frankfurt and Wuhan. It was written mainly when the first author held a "Thousand Expert" Professorship at the Huazhong University of Science and Technology in Wuhan.

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SKU: 26643798743

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Lowell, US
★★★★★ 3
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Color: Llight Gray
Didn't like how fake and tacky it looked.
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Reviewed in the United States on March 16, 2026
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lyric
Bozeman, US
★★★★★ 5
So cutie
Color: Cloud White, Material Type: Paper, PU
This is a bit large for a travel size jewelry box lol I really thought it was going to be a bit smaller than what it was. I can see why some of the ladies in the comments are saying they’re using it as their main jewelry box since they don’t have much jewelry for a standard sized jewelry box. With that being said, it’s cute and CAN be small enough for travel. It fits a lot and I got this one in particular bc I like that it has a bigger lower compartment for larger pieces. It’s a nice quality travel jewelry box. It’ll fit my needs. But if you have a knack for packing small and you value space. I’d say skip on this one or do due diligence to double check the measurements to see if it’s something you’re okay with packing.
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Deena M
Draper, US
★★★★★ 5
Good value
Color: Jelly Pink, Material Type: Paper, PU
This is a great jewelry box for travel or to just keep at home. Very stylish and holds more than it looks like it would.
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Chavely
Boise, US
★★★★★ 5
CUTE
Color: Cloud White, Material Type: Paper, PU
I absolutely love this jewelry organizer! The 2-layer design gives it plenty of space without being bulky, making it perfect for travel. I was able to neatly store my earrings, necklaces, rings, and bracelets without anything getting tangled. The interior is soft and protects my jewelry really well, and the compartments are thoughtfully designed to keep everything in place. The compact size fits easily in my suitcase or handbag, which is a huge plus. The cloud white color looks elegant and makes it feel like a great gift option too. Overall, it’s practical, stylish, and very convenient for keeping jewelry organized on the go. Highly
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Lisa T.
Dallas, US
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I bought myself one and this one was gift for a friend.
Color: Cloud White, Material Type: Paper, PU
Very classy travel jewelry box. Just the size. Made well.
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Reviewed in the United States on May 19, 2026

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