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Clarified what is meant by traditional dynamical systems
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J W
J W
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I am looking for references (or ways to find references) on significant and/or recent applications of techniques in number theory to problems in the areas of dynamical systems and nonlinear dynamics. While there may be overlap with arithmetic dynamics (see, for instance Current Trends and Open Problems in Arithmetic Dynamics by Benedetto, DeMarco, Ingram, Jones, Manes, Silverman & Tucker), I would like examples leaning more towards traditional dynamical systems, in other words differential equations or discrete dynamical systems over the reals or complex numbers.

Note that Lagarias writes in The Unreasonable Effectiveness of Number Theory, Proceedings of Symposia in Applied Mathematics, Volume 46, 1992, American Mathematical Society in the chapter Number Theory and Dynamical Systems:

Number theoretic problems have occurred repeatedly in dynamical systems. This initially seems surprising, since number theory deals with discrete objects.

A citation search using this reference was unrewarding. Other nonrecent papers which might yield a successful citation search would be welcome. Also, useful search terms would be appreciated.

I am looking for references (or ways to find references) on significant and/or recent applications of techniques in number theory to problems in the areas of dynamical systems and nonlinear dynamics. While there may be overlap with arithmetic dynamics (see, for instance Current Trends and Open Problems in Arithmetic Dynamics by Benedetto, DeMarco, Ingram, Jones, Manes, Silverman & Tucker), I would like examples leaning more towards traditional dynamical systems.

Note that Lagarias writes in The Unreasonable Effectiveness of Number Theory, Proceedings of Symposia in Applied Mathematics, Volume 46, 1992, American Mathematical Society in the chapter Number Theory and Dynamical Systems:

Number theoretic problems have occurred repeatedly in dynamical systems. This initially seems surprising, since number theory deals with discrete objects.

A citation search using this reference was unrewarding. Other nonrecent papers which might yield a successful citation search would be welcome. Also, useful search terms would be appreciated.

I am looking for references (or ways to find references) on significant and/or recent applications of techniques in number theory to problems in the areas of dynamical systems and nonlinear dynamics. While there may be overlap with arithmetic dynamics (see, for instance Current Trends and Open Problems in Arithmetic Dynamics by Benedetto, DeMarco, Ingram, Jones, Manes, Silverman & Tucker), I would like examples leaning more towards traditional dynamical systems, in other words differential equations or discrete dynamical systems over the reals or complex numbers.

Note that Lagarias writes in The Unreasonable Effectiveness of Number Theory, Proceedings of Symposia in Applied Mathematics, Volume 46, 1992, American Mathematical Society in the chapter Number Theory and Dynamical Systems:

Number theoretic problems have occurred repeatedly in dynamical systems. This initially seems surprising, since number theory deals with discrete objects.

A citation search using this reference was unrewarding. Other nonrecent papers which might yield a successful citation search would be welcome. Also, useful search terms would be appreciated.

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Source Link
J W
J W
  • 760
  • 9
  • 20

Applications of number theory in dynamical systems

I am looking for references (or ways to find references) on significant and/or recent applications of techniques in number theory to problems in the areas of dynamical systems and nonlinear dynamics. While there may be overlap with arithmetic dynamics (see, for instance Current Trends and Open Problems in Arithmetic Dynamics by Benedetto, DeMarco, Ingram, Jones, Manes, Silverman & Tucker), I would like examples leaning more towards traditional dynamical systems.

Note that Lagarias writes in The Unreasonable Effectiveness of Number Theory, Proceedings of Symposia in Applied Mathematics, Volume 46, 1992, American Mathematical Society in the chapter Number Theory and Dynamical Systems:

Number theoretic problems have occurred repeatedly in dynamical systems. This initially seems surprising, since number theory deals with discrete objects.

A citation search using this reference was unrewarding. Other nonrecent papers which might yield a successful citation search would be welcome. Also, useful search terms would be appreciated.