On the finite dimensionality of integrable deformations of strictly convex integrable billiard tables

Guan Huang; Vadim Kaloshin

doi:10.17323/1609-4514-2019-19-2-307-327

On the finite dimensionality of integrable deformations of strictly convex integrable billiard tables

Guan Huang
, Vadim Kaloshin

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

In this paper, we show that any smooth one-parameter deformations of a strictly convex integrable billiard table Ω₀ preserving the integrability near the boundary have to be tangent to a finite dimensional space passing through Ω₀.

Original language	English
Pages (from-to)	307-327
Number of pages	21
Journal	Moscow Mathematical Journal
Volume	19
Issue number	2
DOIs	https://doi.org/10.17323/1609-4514-2019-19-2-307-327
Publication status	Published - 1 Apr 2019
Externally published	Yes

Keywords

Caustics
Convex billiards
Integrable billiards

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10.17323/1609-4514-2019-19-2-307-327

Cite this

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title = "On the finite dimensionality of integrable deformations of strictly convex integrable billiard tables",

abstract = "In this paper, we show that any smooth one-parameter deformations of a strictly convex integrable billiard table Ω0 preserving the integrability near the boundary have to be tangent to a finite dimensional space passing through Ω0.",

keywords = "Caustics, Convex billiards, Integrable billiards",

author = "Guan Huang and Vadim Kaloshin",

note = "Publisher Copyright: {\textcopyright} 2019 Independent University of Mosow.",

year = "2019",

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doi = "10.17323/1609-4514-2019-19-2-307-327",

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AU - Kaloshin, Vadim

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AB - In this paper, we show that any smooth one-parameter deformations of a strictly convex integrable billiard table Ω0 preserving the integrability near the boundary have to be tangent to a finite dimensional space passing through Ω0.

KW - Caustics

KW - Convex billiards

KW - Integrable billiards

UR - https://www.scopus.com/pages/publications/85067824615

U2 - 10.17323/1609-4514-2019-19-2-307-327

DO - 10.17323/1609-4514-2019-19-2-307-327

M3 - Article

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SP - 307

EP - 327

JO - Moscow Mathematical Journal

JF - Moscow Mathematical Journal

IS - 2

ER -

On the finite dimensionality of integrable deformations of strictly convex integrable billiard tables

Abstract

Keywords

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