1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Irrational Flow yields dense orbits.

  1. Mar 19, 2012 #1
    I have the folloring problem:

    Given the following flow on the torus (θ_1)' = ω_1 and (θ_2)' = ω_2, where ω_1 /ω_2 is irrational then I am asked to show that each trajectory is DENSE. So I need to prove that Given any point p on the torus, any initial condition q, and any ε > 0, then there exists t finite such that the trajectory starting at q passes within a distance epsilon of p, that is to say find a t such that |q - p| < ε.

    My problem is how can I find such a t? Can I prove this by contradiction?

    Thank you very much for your help,


    Juan
     
  2. jcsd
  3. Mar 28, 2012 #2

    morphism

    User Avatar
    Science Advisor
    Homework Helper

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Irrational Flow yields dense orbits.
  1. Irrational demonstration (Replies: 10)

Loading...