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作者：Li, Simin; Shen, Weixiao
作者单位：Chinese Academy of Sciences; University of Science & Technology of China, CAS
摘要：In this paper, we study the Hausdorff dimension of Cantor attractors of smooth interval maps with non-flat critical points. We prove that the Hausdorff dimension is bounded from above by a constant less than 1 which depends only on the number and order of the critical points.
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作者：Brudnyi, Alexander
作者单位：University of Calgary
摘要：In this paper we establish some general results on local behavior of holomorphic functions along complex submanifolds of C-N. As a corollary, we present multi-dimensional generalizations of an important result of Coman and Poletsky on Bernstein type inequalities on transcendental curves in C-2.
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作者：Bates, Peter W.; Lu, Kening; Zeng, Chongchun
作者单位：Michigan State University; Brigham Young University; University System of Georgia; Georgia Institute of Technology
摘要：We investigate the existence of a true invariant manifold given an approximately invariant manifold for an infinite-dimensional dynamical system. We prove that if the given manifold is approximately invariant and approximately normally hyperbolic, then the dynamical system has a true invariant manifold nearby. We apply this result to reveal the global dynamics of boundary spike states for the generalized Allen-Cahn equation.
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作者：Araujo, Carolina; Druel, Stephane; Kovacs, Sandor J.
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); University of Washington; University of Washington Seattle
