Linear Fractional p-Adic and Adelic Dynamical Systems

Abstract

Using an adelic approach we simultaneously consider real and p-adic aspects of dynamical systems whose states are mapped by linear fractional transformations isomorphic to some subgroups of GL (2, Q), SL (2, Q) and SL (2, Z) groups. In particular, we investigate behavior of these adelic systems when fixed points are rational. It is shown that any of these rational fixed points is p-adic indifferent for all but a finite set of primes. Thus only for finite number of p-adic cases a rational fixed point may be attractive or repelling. It is also shown that real and p-adic norms of any nonzero rational fixed point are connected by adelic product formula.

17 pages

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Cited by in corpus (12)

• p-Adic Mathematical Physics
• $p$-Adic Mathematical Physics: The First 30 Years
• Mumford dendrograms
• Renormalization method in $p$-adic $\lambda$-model on the Cayley tree
• Adeles in Mathematical Physics
• Towards effective Lagrangians for adelic strings
• On hyperbolic fixed points in ultrametric dynamics
• On p-Adic Sector of Adelic String
• Estimates of linearization discs in $p$-adic dynamics with application to ergodicity
• Linearization in ultrametric dynamics in fields of characteristic zero - equal characteristic case
• Minimality of p-adic rational maps with good reduction
• Rational map ax+1/x on the projective line over ${\mathbb{Q}}_2$