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Abstract
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In this paper, with Lie bialgebra of bi-symplectic type construct Integrable
Hamiltonian systems for which the Poisson-Lie group G plays the role of phase
space and its dual Lie group ~G
plays the role of symmetry group of the system. We
give the new transformation to exchange the role of phase space and symmetry
group i.e. the Poisson-Lie group ~G
plays the role of phase space and its dual Lie
group G plays the role of symmetry group of the system. Finally, give an example
and then by this transformation, exchange the role of phase space and symmetry
group.
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