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	Aleksandr Lyapunov
		Aleksandr Mikhailovich Lyapunov (Александр Михайлович Ляпунов) (June 6 1857 - November 3 1918, all new style) was a Russian mathematician, mechanician and physicist.
		Lyapunov had already begun to study this stability in his previous two-years attempts at solving the task.
		Lyapunov lectured at the university on themes from theoretical mechanics, integrals of differential equations and the theory of probability.
	www.sciencedaily.com /encyclopedia/aleksandr_lyapunov (1699 words)

	Encyclopedia: Aleksandr Lyapunov (Site not responding. Last check: 2007-10-08)
		Aleksandr Lyapunov File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version.
		In probability theory, Lyapunovs central limit theorem is one of the variants of the central limit theorems.
		Standard Lyapunov logistic fractal with iteration sequence AB Generalized Lyapunov logistic fractal with iteration sequence AABAB In mathematics Lyapunov fractals (also known as Markus-Lyapunov fractals) are bifurcational fractals derived from an extension of the logistic map in which the degree of the growth of the population, r, periodically switches...
	www.nationmaster.com /encyclopedia/Aleksandr-Lyapunov (3697 words)

	Aleksandr Lyapunov: Definition and Links by Encyclopedian.com - All about Aleksandr Lyapunov
		Aleksandr Mikhailovich Lyapunov (Александр Михайлович Ляпунов) (June 6, 1857 - November 3, 1918) was a Russian mathematician, mechanician and physicist.
		Lyapunov wrote his first independent scientific works under the guidance of professor of mechanics, D. Bobilev.
		Lyapunov had lectured already from 1880 at the faculty for mechanics and this had taken him a lot of time.
	www.encyclopedian.com /al/Aleksandr-Lyapunov.html (1640 words)

	ALEKSANDR LYAPUNOV FACTS AND INFORMATION (Site not responding. Last check: 2007-10-08)
		Aleksandr Mikhailovich Lyapunov (ÐÐ»ÐµÐºÑÐ°Ð½Ð´Ñ ÐÐ¸ÑÐ°Ð¹Ð»Ð¾Ð²Ð¸Ñ ÐÑÐ¿ÑÐ½Ð¾Ð²) (June_6 1857 – November_3 1918, all new_style) was a Russian mathematician, mechanician and physicist.
		After the sudden death of his father Aleksandr was educated by his uncle R. Sechenov, brother of the famous philosopher Ivan_Mikhailovich_Sechenov.
		As was said by Vladimir_Andreevich_Steklov, "Chebyshev saw in the young man such an immense research power, that he had dared to lay on him such a toilsome task".
	www.amysflowershop.com /Aleksandr_Lyapunov (1595 words)

	Lyapunov (Site not responding. Last check: 2007-10-08)
		Aleksandr Lyapunov was a school friend of Markov and later a student of Chebyshev.
		His work concentrated on the stability of equilibrium and motion of a mechanical system and the stability of a uniformly rotating fluid.
		Lyapunov's methods, introduced by him in 1899, provide ways of determining the stability of sets of ordinary differential equations.
	www.mathsoc.spb.ru /pantheon/lyapunov (80 words)

	Aleksandr Lyapunov -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		Lyapunov was born in (Click link for more info and facts about Yaroslavl) Yaroslavl, (Click link for more info and facts about Imperial Russia) Imperial Russia.
		Lyapunov had already begun to study this (The quality or attribute of being firm and steadfast) stability in his previous two-years attempts at solving the task.
		Lyapunov lectured at the university on themes from theoretical mechanics, (The result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)) integrals of (An equation containing differentials of a function) differential equations and the (Click link for more info and facts about theory of probability) theory of probability.
	www.absoluteastronomy.com /encyclopedia/A/Al/Aleksandr_Lyapunov.htm (1992 words)

	Lyapunov (Site not responding. Last check: 2007-10-08)
		Aleksandr Mikhailovich began his education at home, then later one of his uncles R M Sechenov prepared him for entering the Gymnasium.
		Lyapunov was not the only one being coached by Sechenov who was teaching his own daughter Natalia Rafailovna Sechenov at the same time.
		Lyapunov established that with variation in the angular velocity of revolution Maclaurin ellipsoids pass into Jacobi ellipsoids.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Lyapunov.html (1165 words)

	References for Lyapunov (Site not responding. Last check: 2007-10-08)
		V A Dobrovol'skii, A M Lyapunov's manuscripts on the theory of ordinary differential equations (Russian), Istor.-Mat.
		J Mawhin, The centennial legacy of Poincaré and Lyapunov in ordinary differential equations, Rend.
		V V Pavlovskaya, A M Lyapunov's investigations on stability of ellipsoidal figures of equilibrium of a rotating fluid mass (Russian), Analytic methods for investigating nonlinear oscillations (Kiev, 1980), 129-138.
	www.mathsoc.spb.ru /pantheon/lyapunov/ref.html (321 words)

	Calendar (events)
		Aleksandr Nikolaevich Nesmeyanov, chemist, president of USSR AS in 1951..
		Georgy Mikhailovich Egorov, submariner, Admiral of Fleet, HSU, Chief of Main Staff of soviet navy, was born.
		Viktor Mikhailovich Glushkov, academician of math (since 1964), director of Institute of Cybernetics of Ukrainian AS, vice president of Ukrainian AS, HSL.
	www.aviation.ru /calendar/?Type=p (2923 words)

	Aleksandr Lyapunov (Site not responding. Last check: 2007-10-08)
		Lyapunov había comenzado ya a estudiar esta estabilidad en sus tentativas anteriores de los dos-años en solucionar la tarea.
		Lyapunov había dado una conferencia ya a partir de 1880 en el departamento de mecánicos y éste lo había tomado mucho tiempo.
		Lyapunov dio una conferencia en la universidad en temas de mecánicos teóricos, de integrales de ecuaciones diferenciales y de la teoría de la probabilidad.
	www.yotor.net /wiki/es/al/Aleksandr%20Lyapunov.htm (1763 words)

	aleksandr (Site not responding. Last check: 2007-10-08)
		Aleksandr Danilovic Aleksandrov's father was the headmaster of a secondary school in St Petersburg and his...
		Aleksandr Sergeevich Pushkin was born on May 26, 1799, in Moscow...
		Aleksandr Pushkin is, by common agreement -- at least among his own compatriots -- the greatest of all Russian writers...
	www.nieddu.biz /russia/aleksandr+.cgi (611 words)

	Knowledge King - List of Russians (Site not responding. Last check: 2007-10-08)
		Aleksandr Solzhenitsyn (born 1918), Nobel Prize for Literature
		Lev Mikhailovich Dovator (1903 - 1941), WWII general and Hero of the Soviet Union
		Aleksandr Ivanovich Pokryshkin (b.1913), WWII fighter pilot, trice Hero of the Soviet Union
	www.knowledgeking.net /encyclopedia/l/li/list_of_russians.html (1092 words)

	technocosm.org - Strange Attractors
		The signature of chaos is that at least one of the Lyapunov exponents is positive.
		Furthermore, the magnitude of the negative exponent has to be greater than the positive one so that initial conditions scattered throughout the basin of attraction contract onto an attractor that occupies a negligible portion of the plane.
		The largest Lyapunov exponent of a system can be computed by taking the difference of the current iteration of x(n) and the current iteration of x(n) plus an epsilon, dx(n), and dividing by the difference of the previous iteration of x(n-1) and previous iteration of x(n-1) + dx(n-1) and taking the natural logarithm.
	technocosm.org /chaos/attr-part2.html (860 words)

	Ðàáîòû ïî òåîðèè ïîòåíöèàëà. Ëÿïóíîâ À.Ì. Libros de Ciencia: Editorial URSS, Moscú. ...
		V universitete, kak govorit sam Aleksandr Mikhajlovich v svoej kratkoj avtobiografii, pomeschennoj v yubilejnom izdanii nashej Akademii nauk, on s osobim uvlecheniem slushal P.L.Chebisheva, kotorij svoimi lektsiyami, a zatem i sovetami okazal suschestvennoe vliyanie na kharakter vsej posleduyuschej uchenoj deyatel'nosti Aleksandra Mikhajlovicha.
		Aleksandr Mikhajlovich sejchas zhe prinyalsya za peredelku pervoj glavi sochineniya.
		Vposledstvii zhe Aleksandr Mikhajlovich s naivnim udivleniem sprashival menya, pochemu tak malo studentov obraschayutsya k nemu za razlichnimi nauchnimi raz'yasneniyami.
	www.urss.ru /cgi-bin/db.pl?cp=&page=Book&id=17644&lang=sp&blang=ru&list=55 (2199 words)

	Encyclopedia: Aleksei Lyapunov (Site not responding. Last check: 2007-10-08)
		He was a distant relative of Aleksandr Lyapunov, and one of Petr Novikov's students.
		A mathematician is a person whose area of study and research is mathematics.
		Aleksandr Mikhailovich Lyapunov (Александр Михайлович Ляпунов) (June 6, 1857 - November 3, 1918, all new style) was a Russian mathematician, mechanician and physicist.
	www.nationmaster.com /encyclopedia/Aleksei-Lyapunov (196 words)

	About the Computer Names (Site not responding. Last check: 2007-10-08)
		Aleksandr Mikhailovich Lyapunov was born on 6 June 1857 at Jaroslavland and in 1876 he became a student in mathematics at St. Petersburg University.
		He published his doctoral thesis (The General Problem of the Stability of Motion) in 1892 and was promoted to professor at Kharkov in 1893.
		On 31 Oct. 1918 she died and on the same day Lyapunov shot himself in the head with a pistol.
	www.control.lth.se /~kurstr/InternDator/names.html (542 words)

	Lyapunov exponents explained
		This Lyapunov exponent is a well known tool in the investigation of dynamic systems (elsewhere I explain how to use it to compute images of the mandelbrot set).
		He was born 6 June 1857 in Yaroslavl (Russia) and died 3 November 1918 in Odessa (he committed suicide three days after the death of his wive).
		The initial value of x usually plays no crucial role: if the Lyapunov exponent of a seed value x is positive, chances are good that it is positive for most other possible seed values.
	www.janthor.de /Lyapunov/explained.html (877 words)

	References for Lyapunov (Site not responding. Last check: 2007-10-08)
		N A Pustovoitov, Theory of the stability of motion after Lyapunov.
		P S Shcherbakov, Alexander Mikhailovitch Lyapunov: on the centenary of his doctoral dissertation on stability of motion, Automatica J. O B Sheinin, Letters from A M Lyapunov to K A Andreev (Russian), Istor.-Mat.
		V V Stepanov and S V Kalinin, Aleksandr Mihailovich Lyapunov: A brief survey of his life and scientific work (Russian), Izvestiya Akad.
	www-gap.dcs.st-and.ac.uk /~history/References/Lyapunov.html (411 words)

	Lyapunov Tilings 1
		Since f is a periodic function and r describes a function shift, the AB-plane itself is periodic.
		The coloration for a given value of A and B is based on the Lyapunov exponent of the function f and starting value x.
		I also added Lyapunov Tilings Part 3 with 30 new tiles and 26 zooms, making a total of 56 additional pictures.
	www.janthor.de /Lyapunov/first.html (372 words)

	Kharkov Mathematical Society (Site not responding. Last check: 2007-10-08)
		However Aleksandr Mikhailovich Lyapunov, a former student of Chebyshev, moved from St Petersburg to Kharkov in 1885 and he remained there for 17 years.
		Because of Lyapunov, mathematical research and reports at Kharkov Mathematical Society meetings reached a much deeper level.
		When Lyapunov left Kharkov in 1902, his former student Vladimir Andreevich Steklov became chairman of the Mathematical Society.
	www-gap.dcs.st-and.ac.uk /~history/Societies/Kharkov.html (579 words)

	Biografías: Aleksandr Mikhailovich Lyapunov (Site not responding. Last check: 2007-10-08)
		Aleksandr Mikhailovich Lyapunov nació el 6 de Junio de 1857 en Yaroslavl, Rusia; murió el 3 de Noviembre de 1918 en Odessa, Rusia, tras darse un tiro el día que su esposa murió.
		Lyapunov dejó una colección de estudios de gran importancia sobre el equilibrio de líquidos rotativos, la probabilidad y la estabilidad de sistemas dinámicos.
		Para salvar estas dificultades, Lyapunov desarrolló su propio concepto de estabilidad.
	eii.unex.es /isa/proyecto/Biografias/Lyapunov.htm (121 words)

	Articles - Lyapunov function (Site not responding. Last check: 2007-10-08)
		In the theory of dynamical systems, and control theory, Lyapunov functions, named after Aleksandr Mikhailovich Lyapunov, are a family of functions that can be used to demonstrate the stability or instability of some state points of a system.
		There is no direct method to obtain a Lyapunov function but there may be tricks to simplify the task.
		The inability to find a Lyapunov function is inconclusive with respect to stability or instability.
	www.poncier.com /articles/Lyapunov_function (185 words)

	Biografía Lyapunov, Aleksandr (Site not responding. Last check: 2007-10-08)
		Aleksandr Lyapunov fue compañero de facultad de Andrei Markov y, posteriormente, alumno de Pafnuty Chebyshev.
		Su labor se concentró en la estabilidad del equilibrio y el movimiento de un sistema mecánico, y la estabilidad de la rotación uniforme de un fluido.
		El 'método de Lyapunov', introducido por él en 1899, proporciona formas de determinar la estabilidad de conjuntos de ecuaciones diferenciales ordinarias.
	mundomatematico.webcindario.com /proyecto_mactutor/biografias/l/bio_lyapunov.html (132 words)

	Lyapunov function (Site not responding. Last check: 2007-10-08)
		In the theory of dynamical systems, and control theory, Lyapunov functions, named after Aleksandr Mikhailovich Lyapunov, are a family of functions that can beused to demonstrate the stability of some state points of a system.
		Not finding one such function does notprove stability or instability, so nothing can be said.
		There is no direct way to obtain a Lyapunov function but there manytricks to simplify the task.
	www.therfcc.org /lyapunov-function-214879.html (96 words)

	Re: [amibroker] Re: Lyapunov exponent and predictability (day)
		Aleksandr Mikhailovich Lyapunov He was born 6 June 1857 in Yaroslavl (Russia) and died 3 November 1918 in Odessa (he committed suicide three days after the death of his wife).
		This would probably be a start for this interesting discussion.
		Hans, Since you already have the AFL code for Hurst Exponent, post it together with a short description for the use to begin with.
	www.purebytes.com /archives/amibroker/2004/msg13248.html (364 words)

	Función de Lyapunov (Site not responding. Last check: 2007-10-08)
		En la teoría de sistemas dinámicos, y la teoría de control, funciones de Lyapunov, nombradas después de Aleksandr Mikhailovich Lyapunov, está una familia de las funciones que se pueden utilizar para demostrar la estabilidad de algunos puntos del estado de un sistema.
		La demostración de la estabilidad requiere encontrar una función de Lyapunov para ese sistema.
		No hay manera directa de obtener una función de Lyapunov pero allí muchos trucos de simplificar la tarea.
	www.yotor.net /wiki/es/fu/Funci%F3n%20de%20Lyapunov.htm (117 words)

	Pronunciation Guide for Mathematics
		A.D. 'hir oh al eg 'zan dree uh
		Lyapunov function often pronounced by English speakers as
		Some English speakers may pronounce her name as
	waukesha.uwc.edu /mat/kkromare/up.html (306 words)

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