Questions tagged [arithmetic-dynamics]

Arithmetic dynamics combines the study of dynamical systems with number theory.

26 questions
42 views

161 views

Why Study Critical Polynomials?

In dynamical systems, I often read about the post-critical orbits. As in take a moduli space of functions $f$ which are self maps. Find general critical points, and see where they orbit. They would ...
236 views

Position of a particle, Newtons Second Law

A particle of mass $40$ kg moves in a straight line such that the force (in newtons) acting on it at time $t$ (in seconds) is given by $$160t^4-320t^2-360$$ If at time $t=0$ its velocity $v$ is given ...
16 views

How can the reaction force of an object be exerted on both bodies?

Assume you have 2 bodies A on top of B. They're both accelerating upwards at 0.5 ms^-2. This is my logic for finding the force exerted on B by A (correct me if I'm wrong) I was told that to find this,...
97 views

Dynamics: circle diffeo with an irrational rotation number and its rational approximation

I need some help in proving the following that arises from the proof of the Denjoy's theorem: Let $f: [0,1] \to [0,1]$ be an orientation preserving circle diffeomorphism topologically conjugated to ...
123 views

116 views

Measure on torus invariant under multiplication

Let $T: [0,1] \rightarrow [0,1]$ be a multiplication by $\beta >1$ mod $1$. Show that $h(x) d x$ is $T$-invariant where $$h (x) = \sum_{n \geq 0} \beta^{-n} \chi _{[0,T^n (1)]} (x)$$ ($\chi$ is ...
275 views