A First Course in Dynamics: with a Panorama of Recent Developments

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Control of an uncertain fractional-order Liu system via fuzzy fractional-order sliding mode control (2012, background): “Although there is no universally accepted mathematical definition of chaos, a commonly used definition says that, for a dynamical system to be classified as chaotic, it must have the following properties (Hasselblatt and Katok, 2003): 1.”
Degree-growth of monomial maps (2006, background): “ultiplicativity property. The relevant property is that for all rational maps f,g, deg(f ◦g) ≤ deg(f)deg(g). A ﬁrst consequence of this inequality (via a standard argument; e.g., Proposition 9.6.4 of [HK]) is that 1 N logdeg(f(N)) converges to a limit, called the (BellonViallet) algebraic entropy of”