A convenient expression of the time-derivative zn(k)(t) , of arbitrary order k, of the zero z n (t) of a time-dependent polynomial p N (z;t) of arbitrary degree N in z, and

DOI10.1080/14029251.2016.1237197zbMath1421.70019OpenAlexW2520676195MaRDI QIDQ5231040

Mario Bruschi, Francesco Calogero

Publication date: 29 August 2019

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/14029251.2016.1237197

zbMATH Keywords

solvable dynamical systemssolvable many-body problemsisochronous many-body problemstime-derivatives of the zeros of time-dependent polynomialstime-derivatives of time-dependent polynomials

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) (n)-body problems (70F10)

Related Items (6)

Zeros of entire functions and related systems of infinitely many nonlinearly coupled evolution equations ⋮ Zeros of rational functions and solvable nonlinear evolution equations ⋮ Time-dependent polynomials with \textit {one double} root, and related new solvable systems of nonlinear evolution equations ⋮ Generations of solvable discrete-time dynamical systems ⋮ Time-dependent polynomials with one multiple root and new solvable dynamical systems ⋮ Polynomials with multiple zeros and solvable dynamical systems including models in the plane with polynomial interactions

Cites Work

• Understanding complex dynamics by means of an associated Riemann surface
• Yet another class of \textit{new solvable} \(N\)-body problems of goldfish type
• Newtonian dynamics in the plane corresponding to straight and cyclic motions on the hyperelliptic curve \(\mu^{2}= \nu^{n}-1, n \in \mathbb Z\): ergodicity, isochrony and fractals
• New Solvable Variants of the Goldfish Many-Body Problem
• Novel isochronous N-body problems featuring N arbitrary rational coupling constants
• Asymptotically isochronous systems
• A new solvable many-body problem of goldfish type
• Novel solvable many-body problems
• A Solvable N-body Problem of Goldfish Type Featuring N² Arbitrary Coupling Constants
• Isochronous Systems
• Towards a theory of chaos explained as travel on Riemann surfaces
• The transition from regular to irregular motions, explained as travel on Riemann surfaces

This page was built for publication: A convenient expression of the time-derivative zn(k)(t) , of arbitrary order k, of the zero z _n (t) of a time-dependent polynomial p _N (z;t) of arbitrary degree N in z, and