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  "body": "\n## Summary\n\nArithmetic dynamics studies the number-theoretic properties of points under iteration of polynomial and rational maps, and more generally of self-maps of algebraic varieties.\nTypical questions ask which rational or algebraic points are [[periodic|T75CZ5H47N]] or preperiodic.\nOthers ask how the [[height|F1FF505PWH]] of a point grows along its orbit, and how orbits behave modulo primes or over $p$-adic fields.\nIt combines complex dynamics with Diophantine geometry.\nMany of its conjectures are dynamical analogues of results on elliptic curves and abelian varieties, where torsion points play the role of preperiodic points.\n\n## Explanations\n\n### L1 human\n\nTake a simple rule like $x \\mapsto x^2 - 1$ and apply it again and again to a fraction.\nSome starting values, such as $0$, run in a cycle: $0 \\mapsto -1 \\mapsto 0$.\nMost starting values, such as $2$, produce numbers with more and more digits: $2, 3, 8, 63, \\ldots$.\nArithmetic dynamics asks which starting values give cycles, how fast the digits grow, and what such patterns look like over other number systems.\n",
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