Joseph Liouville

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Liouville, Joseph


Born Mar. 24, 1809, in St. Orner; died Sept. 8, 1882, in Paris. French mathematician. Member of the Paris Academy of Sciences (1839).

Liouville was a professor at the Ecole Polytechnique (from 1833) and the Collège de France (from 1839). He constructed the theory of elliptic functions, which he viewed as doubly periodic functions of a complex variable. He also studied the boundary-value problem for second-order linear differential equations (the Sturm-Liouville problem). Liouville proved the existence of transcendental numbers and gave an actual construction of such numbers. He established a fundamental theorem in mechanics (Liouville’s theorem) on the integration of the canonical equations of dynamics.


“Discours, prononcés aux funérailles de M. Liouville.” Comptes rendus hébdomadaires des séances de l’Académie des Sciences de Paris, 1882, vol. 95, pp. 467–71.
Synge, J. L. Classical Dynamics. Moscow, 1963. (Translated from English.)
References in periodicals archive ?
A real number [xi] is called a Liouville number, if there exist infinitely many rational numbers [([p.
Saarloos[3] shown that the density function (mass, momentum and energy fields) obeys a Liouville equation for hydrodynamics ideal fluid.
Para tal, partimos da equacao de Liouville e, assumindo a validade de outras duas equacoes, chegamos a equacao de Schrodinger.
Two and four dimensional holomorphic blocks can be reinterpreted as conformal blocks in Liouville theory through an established correspondence between supersymmetric gauge theories and Liouville theory.
On variations of the Liouville constant which are also Liouville numbers Diego MARQUES and Carlos Gustavo MOREIRA Communicated by Masaki KASHIWARA, M.
Bikulciene, "The solitary solution of the Liouville equation produced by the Exp-function method holds not for all initial conditions", Computers and Mathematics with Applications, vol.
Particularly, they compared the series of geophysical excitations with the observed nutation angles by using numerical integration of the Brzezinski (1994) broadband Liouville second-order differential equations.
For each fixed x, we apply the Liouville transformation [7, 8, 29-31, 33]:
One of the most intriguing aspects of examining Liouville states with quantum states is the striking similarity between phenomena exhibited in Liouville mechanics and what is observed in pure quantum states that are not seen in systems involving states of complete knowledge.
In the last years, the inverse nodal problem and fractional calculus for Sturm Liouville problem has been studied by several authors Browne and Sleeman (1996), Yang (1997), Cheng et al.
Esta teoria ya habia sido esbozada por Galois, difundida por Liouville y sistematizada por Camille Jordan como grupo de transformaciones en el que estudiaba las sustituciones y las ecuaciones algebraicas.