Results 1 to 4 of 4

Math Help - How to find all the orbits of a permutation defined by a function?

  1. #1
    Newbie
    Joined
    Sep 2011
    Posts
    2

    How to find all the orbits of a permutation defined by a function?

    I have a function, where T sends Z-->Z, where T(x)=x+5

    The only thing I could think of for defining the orbits were orbits like cyclic subgroups under the operation of T (like for instance <1>={1, 6, 11 ...}

    but not only would those orbits be infinite, I don't think they are right.

    so does anyone have some sort of help to offer on finding orbits of a function with no parameters?

    -jackie
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21

    Re: How to find all the orbits of a permutation defined by a function?

    Quote Originally Posted by jackie213 View Post
    I have a function, where T sends Z-->Z, where T(x)=x+5

    The only thing I could think of for defining the orbits were orbits like cyclic subgroups under the operation of T (like for instance <1>={1, 6, 11 ...}

    but not only would those orbits be infinite, I don't think they are right.

    so does anyone have some sort of help to offer on finding orbits of a function with no parameters?

    -jackie
    Orbits in what sense of the word? There isn't an action mentioned. If you mean though the orbit in the sense of say dynamics (i.e. iteratives of the function) then it's pretty easy to see that T(x)=T(y) if and only if 5\mid x-y if and only if [x]_5=[y]_5 where [\cdot]_5 is the residue class modulo five. Does that help?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2011
    Posts
    2

    Re: How to find all the orbits of a permutation defined by a function?

    That seems to make sense I am just wary because I have never seen it with not being strictly numerical values.

    And just to make sure we're on the same page, I mean orbits in terms of cycles/equivalence classes in abstract.

    And thank you very much for responding!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21

    Re: How to find all the orbits of a permutation defined by a function?

    Quote Originally Posted by jackie213 View Post
    That seems to make sense I am just wary because I have never seen it with not being strictly numerical values.

    And just to make sure we're on the same page, I mean orbits in terms of cycles/equivalence classes in abstract.

    And thank you very much for responding!
    Yes, I think we're on the same wave length.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: October 19th 2011, 04:49 AM
  2. Replies: 3
    Last Post: February 21st 2011, 08:01 AM
  3. find where the slope is defined..
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 23rd 2009, 04:52 PM
  4. Replies: 2
    Last Post: August 5th 2009, 10:20 AM
  5. Replies: 1
    Last Post: June 25th 2009, 08:01 PM

Search Tags


/mathhelpforum @mathhelpforum