Tips of Tongues in the Double Standard Family
| Autor: | Adam L. Epstein, Kuntal Banerjee, Xavier Buff, Jordi Canela |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Warwick Mathematics Institute (WMI), University of Warwick [Coventry], Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), ANR-11-LABX-0040,CIMI,Centre International de Mathématiques et d'Informatique (de Toulouse)(2011) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Degree (graph theory)
Applied Mathematics [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] 010102 general mathematics Zero (complex analysis) General Physics and Astronomy Statistical and Nonlinear Physics Multiplicity (mathematics) Dynamical Systems (math.DS) Lambda 01 natural sciences 010305 fluids & plasmas Combinatorics 0103 physical sciences FOS: Mathematics 0101 mathematics Mathematics - Dynamical Systems Mathematical Physics Mathematics |
| Zdroj: | Dipòsit Digital de Documents de la UAB Universitat Autònoma de Barcelona Nonlinearity Nonlinearity, 2021, 34 (12), pp.8174-8191 |
| ISSN: | 0951-7715 1361-6544 |
| Popis: | We answer a question raised by Misiurewicz and Rodrigues concerning the family of degree two circle maps F λ : R / Z → R / Z defined by F λ ( x ) ≔ 2 x + a + b π sin ( 2 π x ) with λ ≔ ( a , b ) ∈ R / Z × ( 0 , 1 ) . We prove that if F λ ◦ n − i d has a zero of multiplicity three in R / Z , then there is a system of local coordinates ( α , β ) : W → R 2 defined in a neighborhood W of λ, such that α(λ) = β(λ) = 0 and F μ ◦ n − i d has a multiple zero with μ ∈ W if and only if β 3(μ) = α 2(μ). This shows that the tips of tongues are regular cusps. |
| Databáze: | OpenAIRE |
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