Ad
related to: lyapunov exponents math theoryeducation.com has been visited by 100K+ users in the past month
This site is a teacher's paradise! - The Bender Bunch
- Worksheet Generator
Use our worksheet generator to make
your own personalized puzzles.
- Guided Lessons
Learn new concepts step-by-step
with colorful guided lessons.
- 20,000+ Worksheets
Browse by grade or topic to find
the perfect printable worksheet.
- Printable Workbooks
Download & print 300+ workbooks
written & reviewed by teachers.
- Worksheet Generator
Search results
Results from the WOW.Com Content Network
Lyapunov proved that if the system of the first approximation is regular (e.g., all systems with constant and periodic coefficients are regular) and its largest Lyapunov exponent is negative, then the solution of the original system is asymptotically Lyapunov stable. Later, it was stated by O. Perron that the requirement of regularity of the ...
In mathematics, the multiplicative ergodic theorem, or Oseledets theorem provides the theoretical background for computation of Lyapunov exponents of a nonlinear dynamical system. It was proved by Valery Oseledets (also spelled "Oseledec") in 1965 and reported at the International Mathematical Congress in Moscow in 1966.
Lyapunov stability Lyapunov exponent Lyapunov central limit theorem Lyapunov vector Qualitative theory of differential equations: Scientific career: Fields: Applied mathematics: Institutions: Saint Petersburg State University Russian Academy of Sciences Kharkov University: Thesis: The general problem of the stability of motion (1892) Doctoral ...
The mathematical theory of stability of motion, founded by A. M. Lyapunov, considerably anticipated the time for its implementation in science and technology. Moreover Lyapunov did not himself make application in this field, his own interest being in the stability of rotating fluid masses with astronomical application.
The real parts of the Floquet exponents are called Lyapunov exponents. The zero solution is asymptotically stable if all Lyapunov exponents are negative, Lyapunov stable if the Lyapunov exponents are nonpositive and unstable otherwise. Floquet theory is very important for the study of dynamical systems, such as the Mathieu equation.
In the theory of ordinary differential equations (ODEs), Lyapunov functions, named after Aleksandr Lyapunov, are scalar functions that may be used to prove the stability of an equilibrium of an ODE. Lyapunov functions (also called Lyapunov’s second method for stability) are important to stability theory of dynamical systems and control theory .
The rate of separation depends on the orientation of the initial separation vector, so a whole spectrum of Lyapunov exponents can exist. The number of Lyapunov exponents is equal to the number of dimensions of the phase space, though it is common to just refer to the largest one. For example, the maximal Lyapunov exponent (MLE) is most often ...
The study of billiards which are kept out of a region, rather than being kept in a region, is known as outer billiard theory. The motion of the particle in the billiard is a straight line, with constant energy, between reflections with the boundary (a geodesic if the Riemannian metric of the billiard table is not flat).
Ad
related to: lyapunov exponents math theoryeducation.com has been visited by 100K+ users in the past month
This site is a teacher's paradise! - The Bender Bunch