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Generalized Lyapunov exponents corresponding to higher derivatives. (English) Zbl 0778.58036
Let $$f:I\to I$$ be a differentiable map on some $$I\subset\mathbb{R}$$. The paper introduces the expression $$\lim_{n\to\infty}{1\over n}\log|{d^ p\over dx^ p}f^ n(x)|$$ to be the $$p$$th order Lyapunov exponent. The notion is extended to $$f:M\to M$$, $$M$$ an $$n$$-dimensional manifold, expressing the $$p$$th derivative of $$f$$ by the $$p$$th derivative of the induced map in a chart. The cases of fixed points and of periodic orbits of $$f$$ are discussed in some detail for both the one- and the $$n$$- dimensional case, providing expressions for the $$p$$th order exponents in terms of the first order exponents.

##### MSC:
 37A99 Ergodic theory 37E99 Low-dimensional dynamical systems
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##### References:
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