A metric of mutual energy and unlikely intersections for dynamical systems

2017/08/28 by Paul Fili, Fili, Paul · 4 citations
Mathematics · Physics and Astronomy · #11G50 #31A15 #37P05 #37P30 #37P50 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Quantum chaos and dynamical systems #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1708.08403

openalex publication_date 2017/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a metric of mutual energy for adelic measures associated to the Arakelov-Zhang pairing. Using this metric and potential theoretic techniques involving discrete approximations to energy integrals, we prove an effective bound on a problem of Baker and DeMarco on unlikely intersections of dynamical systems, specifically, for the set of complex parameters c for which z=0 and 1 are both preperiodic under iteration of f_c(z)=z² + c.

Cited by

• Areal Weil Heights
• A quantitative dynamical Zhang fundamental inequality and Bogomolov-type problems
• Uniform unlikely intersections for unicritical polynomials
• The Uniform Boundedness and Dynamical Lang Conjectures for polynomials

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