Multiple Periodic Solutions and Fractal Attractors of Differential Equations with n-Valued Impulses
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F20%3A73602184" target="_blank" >RIV/61989592:15310/20:73602184 - isvavai.cz</a>
Result on the web
<a href="https://www.mdpi.com/2227-7390/8/10/1701/htm" target="_blank" >https://www.mdpi.com/2227-7390/8/10/1701/htm</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/math8101701" target="_blank" >10.3390/math8101701</a>
Alternative languages
Result language
angličtina
Original language name
Multiple Periodic Solutions and Fractal Attractors of Differential Equations with n-Valued Impulses
Original language description
Ordinary differential equations with n-valued impulses are examined via the associated Poincare translation operators from three perspectives: (i) the lower estimate of the number of periodic solutions on the compact subsets of Euclidean spaces and, in particular, on tori; (ii) weakly locally stable (i.e., non-ejective in the sense of Browder) invariant sets; (iii) fractal attractors determined implicitly by the generating vector fields, jointly with Devaney's chaos on these attractors of the related shift dynamical systems. For (i), the multiplicity criteria can be effectively expressed in terms of the Nielsen numbers of the impulsive maps. For (ii) and (iii), the invariant sets and attractors can be obtained as the fixed points of topologically conjugated operators to induced impulsive maps in the hyperspaces of the compact subsets of the original basic spaces, endowed with the Hausdorff metric. Five illustrative examples of the main theorems are supplied about multiple periodic solutions (Examples 1-3) and fractal attractors (Examples 4 and 5).
Czech name
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Czech description
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Classification
Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematics
ISSN
2227-7390
e-ISSN
—
Volume of the periodical
8
Issue of the periodical within the volume
10
Country of publishing house
CH - SWITZERLAND
Number of pages
21
Pages from-to
"1701-1"-"1701-21"
UT code for WoS article
000586911300001
EID of the result in the Scopus database
2-s2.0-85092915848