mathematics, in the study of dynamical systems, the Hartman–Grobman theorem or linearisation theorem is a theorem about the local behaviour of dynamical systems...

and graphic artist Philip Hartman (1915–2015), American mathematician, known a.o. for the Hartman–Grobman theorem Piet Hartman (1922–2021), Dutch crystallographer...

whose eigenvalues characterize the behavior of the nearby points (Hartman–Grobman theorem). More precisely, if all eigenvalues are negative real numbers...

and its variants outside topology. It can be used to prove the Hartman-Grobman theorem, which describes the qualitative behaviour of certain differential...

University working on differential equations who introduced the Hartman–Grobman theorem. He served as Chairman of the Mathematics Department at Johns Hopkins...

_{0}} is a stationary point (also called a steady state). By the Hartman–Grobman theorem, the behavior of the system near a stationary point is related...

eigenvalues of the linearization have nonzero real part), then the Hartman-Grobman theorem guarantees that these eigenvalues and eigenvectors completely characterise...

(cellular automata) Hartman–Grobman theorem (dynamical systems) Kolmogorov–Arnold–Moser theorem (dynamical systems) Krylov–Bogolyubov theorem (dynamical systems)...

invariance principle Lyapunov–Malkin theorem Markus–Yamabe conjecture Libration point orbit Hartman–Grobman theorem Perturbation theory Stability theory...

the dynamics is called elliptic. In the hyperbolic case, the Hartman–Grobman theorem gives the conditions for the existence of a continuous function...

hyperbolic critical points or elementary critical points. The Hartman–Grobman theorem states that the orbit structure of a dynamical system in a neighbourhood...

unstable if and only if the coexistence-steady-state exists. By the Hartman–Grobman theorem, one can determine the stability of the steady states by approximating...

the number of predators, and α, β, γ and δ are constants. By the Hartman–Grobman theorem the non-linear system is topologically equivalent to a linearization...

Physica D, 84:357–397, 1995. Aulbach, B.; Wanner, T. (2000). "The Hartman–Grobman theorem for Caratheodory-type differential equations in Banach spaces"...

qualitatively, we may be able to know the asymptotic solution, such as Hartman-Grobman results and more. Occasionally, polar coordinates may yield standard...