Discontinuities Cause Essential Spectrum on Surfaces

IF 1.3 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Annales Henri Poincaré Pub Date : 2024-10-12 DOI:10.1007/s00023-024-01499-y

Oliver Butterley, Giovanni Canestrari, Roberto Castorrini

引用次数: 0

Abstract

Two-dimensional maps with discontinuities are considered. It is shown that, in the presence of discontinuities, the essential spectrum of the transfer operator is large whenever it acts on a Banach space with norm that is stronger than \(L^\infty \) or \(BV\). Three classes of examples are introduced and studied, both expanding and partially expanding. In two dimensions, there is complication due to the geometry of the discontinuities, an issue not present in the one-dimensional case and which is explored in this work.

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不连续性在表面上产生本质光谱

考虑具有不连续的二维映射。结果表明，在不连续的情况下，只要传递算子作用于范数大于\(L^\infty \)或\(BV\)的Banach空间，它的本质谱就很大。介绍并研究了三种类型的例子，即展开式和部分展开式。在二维中，由于不连续性的几何形状而存在复杂性，这是一维情况中不存在的问题，并且在本工作中进行了探讨。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annales Henri Poincaré 物理-物理：粒子与场物理

CiteScore

3.00

自引率

6.70%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society. The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.