Solvable Initial Value Problems Ruled by Discontinuous Ordinary Differential Equations
O Bournez, R Gozzi - arXiv preprint arXiv:2405.00165, 2024 - arxiv.org
O Bournez, R Gozzi
arXiv preprint arXiv:2405.00165, 2024•arxiv.orgWe study initial value problems having dynamics ruled by discontinuous ordinary differential
equations with the property of possessing a unique solution. We identify a precise class of
such systems that we call\emph {solvable intitial value problems} and we prove that for this
class of problems the unique solution can always be obtained analytically via transfinite
recursion. We present several examples including a nontrivial one whose solution yields, at
an integer time, a real encoding of the halting set for Turing machines; therefore showcasing …
equations with the property of possessing a unique solution. We identify a precise class of
such systems that we call\emph {solvable intitial value problems} and we prove that for this
class of problems the unique solution can always be obtained analytically via transfinite
recursion. We present several examples including a nontrivial one whose solution yields, at
an integer time, a real encoding of the halting set for Turing machines; therefore showcasing …
We study initial value problems having dynamics ruled by discontinuous ordinary differential equations with the property of possessing a unique solution. We identify a precise class of such systems that we call \emph{solvable intitial value problems} and we prove that for this class of problems the unique solution can always be obtained analytically via transfinite recursion. We present several examples including a nontrivial one whose solution yields, at an integer time, a real encoding of the halting set for Turing machines; therefore showcasing that the behavior of solvable systems is related to ordinal Turing computations.
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