Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounded height in families of dynamical systems   Let a and b be algebraic numbers such that exactly one of a and b is an
algebraic integer, and let f_t(z):=z^2+t be a family of polynomials
parametrized by t. We prove that the set of all algebraic numbers t for which
there exist positive integers m and n such that f_t^m(a)=f_t^n(b) has bounded
Weil height. This is a special case of a more general result supporting a new
bounded height conjecture in dynamics. Our results fit into the general setting
of the principle of unlikely intersections in arithmetic dynamics.

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The categories of this paper are: econ
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The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org