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Anal."],"published-print":{"date-parts":[[2020,1]]},"abstract":"<jats:p>For regular $SU(3)$ Toda systems defined on Riemann surface, we initiate the study of bubbling solutions if parameters $(\\rho_1^k,\\rho_2^k)$ are both tending to critical positions: $(\\rho_1^k,\\rho_2^k)\\to (4\\pi, 4\\pi N)$ or $(4\\pi N, 4\\pi)$ ($N&gt;0$ is an integer). We prove that there are at most three formations of bubbling profiles, and for each formation we identify leading terms of $\\rho_1^k-4\\pi$ and $\\rho_2^k-4\\pi N$, locations of blow-up points, and comparison of bubbling heights with sharp precision. The results of this article will be used as substantial tools for a number of degree counting theorems and critical point at infinity theory in the future.<\/jats:p>","DOI":"10.1137\/20m131031x","type":"journal-article","created":{"date-parts":[[2020,8,11]],"date-time":"2020-08-11T14:25:49Z","timestamp":1597155949000},"page":"3738-3776","source":"Crossref","is-referenced-by-count":2,"title":["Estimates of Bubbling Solutions of $SU(3)$ Toda Systems at Critical Parameters. Part 1"],"prefix":"10.1137","volume":"52","author":[{"given":"Lina","family":"Wu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4792-3542","authenticated-orcid":true,"given":"Lei","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2020,8,11]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2013.11.006"},{"key":"atypb2","volume-title":"A Moser-Trudinger Inequality for the Singular Toda System, preprint, arXiv:1307.3921","author":"Battaglia L.","year":"2013"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(91)90026-2"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160410302"},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"J. Bolton and L. M. 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