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nLab > Latest Changes: dynamical system

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  1. added a reference to Dynamical Systems and Sheaves by Schultz, Spivak, and Vasilakopoulou

    Joe M

    diff, v8, current

    • CommentRowNumber2.
    • CommentAuthorMarc
    • CommentTimeAug 29th 2019

    changed the broken link to pdf of Lawere reprint and added link to the reprint page (in case the direct link to pdf changes in the future).

    diff, v9, current

    • CommentRowNumber3.
    • CommentAuthorGuest
    • CommentTimeJun 26th 2021

    Question: does this current definition of dynamical system generalise to dynamical systems over higher geometric structures such as smooth infinity-stacks, which are not sets in a cohesive type theory context?

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJun 26th 2021
    • (edited Jun 26th 2021)

    Currently, the page (which is a little thin) states nothing but a smooth ℝ 1\mathbb{R}^1-group action. One would also want to refer to ℤ\mathbb{Z}-actions as dynamical systems, at times. Generally, one can of fix any group object GG encoding the desired type of (space-)time evolution and then regard GG-action objects as dynamical systems in the given ambient category.

    At this point this is really just “transformation group theory” with an interpretation of “dynamics” tacked onto it, dictated by the intended application.

    Now, group actions, of course, generalize far and wide, in particular to infinity-actions of ∞\infty-group stacks on ∞\infty-stacks of any sort. Yes.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeAug 17th 2023

    added this pointer:

    • David Jaz Myers, A general definition of open dynamical systems, talk at MIT Category Theory Seminar (2020) [video:YT]

    diff, v14, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeOct 25th 2023
    • (edited Oct 25th 2023)

    I have reworded the Idea section (it used to claim, since revision 1, that dynamical systems are all given by an action of ℝ\mathbb{R}. I made that but one example of general actions by a monoid).

    Added pointer to:

    diff, v15, current

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