Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the ergodicity of geodesic flows on surfaces without focal points   In this article, we study the ergodicity of the geodesic flows on surfaces
with no focal points. Let $M$ be a smooth connected and closed surface equipped
with a $C^\infty$ Riemannian metric $g$, whose genus $\mathfrak{g} \geq 2$.
Suppose that $(M,g)$ has no focal points. We prove that the geodesic flow on
the unit tangent bundle of $M$ is ergodic with respect to the Liouville
measure, under the assumption that the set of points on $M$ with negative
curvature has at most finitely many connected components.

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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con