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http://hdl.handle.net/1942/34091
Title: | Fractal analysis of planar nilpotent singularities and numerical applications | Authors: | Horvat Dmitrovic, Lana HUZAK, Renato Vlah, Domagoj Županovic´, Vesna |
Issue Date: | 2021 | Publisher: | ACADEMIC PRESS INC ELSEVIER SCIENCE | Source: | JOURNAL OF DIFFERENTIAL EQUATIONS, 293, p. 1-22 | Abstract: | The goal of our work is to give a complete fractal classification of planar analytic nilpotent singularities. For the classification, we use the notion of box dimension of (two-dimensional) orbits on separatrices generated by the unit time map. We also show how the box dimension of the one-dimensional orbit generated by the Poincaré map, defined on the characteristic curve near the nilpotent center/focus, reveals an upper bound for the number of limit cycles near the singularity. We introduce simple formulas for numerical calculation of the box dimension of one-and two-dimensional orbits and apply them to nilpotent singularities. | Keywords: | Keyword: nilpotent singularity;box dimension;unit-time map;Poincaré map | Document URI: | http://hdl.handle.net/1942/34091 | ISSN: | 0022-0396 | e-ISSN: | 1090-2732 | DOI: | 10.1016/j.jde.2021.05.015 | ISI #: | 000663792600002 | Rights: | 2021 Elsevier Inc. All rights reserved | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2022 |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
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1-s2.0-S0022039621002990-main.pdf Restricted Access | Published version | 958.49 kB | Adobe PDF | View/Open Request a copy |
unitTime-22_09_2020.pdf | Peer-reviewed author version | 761.48 kB | Adobe PDF | View/Open |
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