Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bifurcations in the Space of Exponential Maps   This article investigates the parameter space of the exponential family
$z\mapsto \exp(z)+\kappa$. We prove that the boundary (in $\C$) of every
hyperbolic component is a Jordan arc, as conjectured by Eremenko and Lyubich as
well as Baker and Rippon. In fact, we prove the stronger statement that the
exponential bifurcation locus is connected in $\C$, which is an analog of
Douady and Hubbard's celebrated theorem that the Mandelbrot set is connected.
We show furthermore that $\infty$ is not accessible through any nonhyperbolic
("queer") stable component.
  The main part of the argument consists of demonstrating a general "Squeezing
Lemma", which controls the structure of parameter space near infinity. We also
prove a second conjecture of Eremenko and Lyubich concerning bifurcation trees
of hyperbolic components.

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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg