Kahan discretisation of a cubic Hamiltonian system

Thomas Kecker; Galina Filipuk

Kahan discretisation of a cubic Hamiltonian system

Thomas Kecker, Galina Filipuk

School of Mathematics & Physics

University of Warsaw

Research output: Contribution to conference › Abstract › peer-review

Abstract

We apply Kahan’s discretisation method, also known as the Hirota-Kimura method or Runge-Kutta method, to a cubic Hamiltonian system of Painlevé type. The system being non-autonomous it is not clear from the start whether discretisation will preserve integrability. Although the resulting discrete system is non-integrable, by introducing a parameter into the equations one obtains a system with reduced (though non-zero) algebraic entropy.

Original language	English
Publication status	Published - 11 Dec 2017
Event	14th International Conference Dynamical Systems - Theory and Applications - Łódź, Poland Duration: 11 Dec 2017 → 14 Dec 2017 https://www.dys-ta.com/

Conference

Conference	14th International Conference Dynamical Systems - Theory and Applications
Abbreviated title	DSTA 2017
Country/Territory	Poland
City	Łódź
Period	11/12/17 → 14/12/17
Internet address	https://www.dys-ta.com/

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title = "Kahan discretisation of a cubic Hamiltonian system",

abstract = "We apply Kahan{\textquoteright}s discretisation method, also known as the Hirota-Kimura method or Runge-Kutta method, to a cubic Hamiltonian system of Painlev{\'e} type. The system being non-autonomous it is not clear from the start whether discretisation will preserve integrability. Although the resulting discrete system is non-integrable, by introducing a parameter into the equations one obtains a system with reduced (though non-zero) algebraic entropy.",

author = "Thomas Kecker and Galina Filipuk",

year = "2017",

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day = "11",

language = "English",

note = "14th International Conference Dynamical Systems - Theory and Applications, DSTA 2017 ; Conference date: 11-12-2017 Through 14-12-2017",

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TY - CONF

T1 - Kahan discretisation of a cubic Hamiltonian system

AU - Kecker, Thomas

AU - Filipuk, Galina

PY - 2017/12/11

Y1 - 2017/12/11

N2 - We apply Kahan’s discretisation method, also known as the Hirota-Kimura method or Runge-Kutta method, to a cubic Hamiltonian system of Painlevé type. The system being non-autonomous it is not clear from the start whether discretisation will preserve integrability. Although the resulting discrete system is non-integrable, by introducing a parameter into the equations one obtains a system with reduced (though non-zero) algebraic entropy.

AB - We apply Kahan’s discretisation method, also known as the Hirota-Kimura method or Runge-Kutta method, to a cubic Hamiltonian system of Painlevé type. The system being non-autonomous it is not clear from the start whether discretisation will preserve integrability. Although the resulting discrete system is non-integrable, by introducing a parameter into the equations one obtains a system with reduced (though non-zero) algebraic entropy.

M3 - Abstract

T2 - 14th International Conference Dynamical Systems - Theory and Applications

Y2 - 11 December 2017 through 14 December 2017

ER -

Kahan discretisation of a cubic Hamiltonian system

Abstract

Conference

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