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Eupolars and their Bialternality Grid

icon-email Jean Ecalle

Abstract

This monograph is almost entirely devoted to the flexion structure generated by a flexion unit E or the conjugate unit O, with special emphasis on the polar specialization of the units ({``eupolar structure''}).

 (i) We first state and prove the main facts (some of them new) about the central pairs of {bisymmetrals} pal∙/pil∙ and par∙/pir∙ and their even/odd factors, by relating these to four remarkable series of {alternals} {rer∙}, {ler∙}, {her∙}, {ke2r∙}, and that too in a way that treats the swappees pal∙ and pil∙ (resp. par∙ and pir∙) as they should be treated, i.e. on a strictly equal footing.

 (ii) Next, we derive from the central bisymmetrals two series of {bialternals}, distinct yet partially (and rather mysteriously) related.

 (iii) Then, as a first step towards a complete description of the eupolar structure, we introduce the notion of {bialternality grid} and present some facts and conjectures suggested by our (still ongoing) computations.

(iv) Lastly, two complementary sections have been added, to show which features of the eupolar structure survive, change form or altogether diappear when one moves on to the next two cases in order of importance: eutrigonometric and polynomial.

Viện Toán học, Viện Hàn lâm Khoa học và Công nghệ Việt Nam

Địa chỉ: Số 18 đường Hoàng Quốc Việt, quận Cầu Giấy, Hà Nội

Điện thoại: 024 37563474 - Fax: 024 37564303

Email: vientoan@math.ac.vn

Viện nghiên cứu cao cấp về toán Hội Toán học Mỹ MathScinet Thư viện số (VAST) Arxiv
Lịch hoạt động chung Lịch sử dụng phòng, hội trường, hội thảo Ảnh hoạt động
Giới thiệu Đăng nhập Đăng ký tài khoản Quên mật khẩu Chính sách bảo mật
Messages2TimelineExceptionsViews8RouteQueries108Models431MailsGateSessionRequest
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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