By Xiang Zhang

This is the 1st e-book to systematically nation the basic concept of integrability and its improvement of normal differential equations with emphasis at the Darboux idea of integrability and native integrability including their functions. It summarizes the classical result of Darboux integrability and its glossy improvement including their comparable Darboux polynomials and their purposes reduce Liouville and hassle-free integrabilty and within the center—focus challenge, the weakened Hilbert sixteenth challenge on algebraic restrict cycles and the worldwide dynamical research of a few sensible types in fields reminiscent of physics, mechanics and biology.

Although it may be used as a textbook for graduate scholars in dynamical platforms, it's meant as supplementary analyzing for graduate scholars from arithmetic, physics, mechanics and engineering in classes relating to the qualitative conception, bifurcation concept and the speculation of integrability of dynamical systems.

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