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mathematical physics > dynamical systems theory > dynamical system > Lefschetz zeta function

number > number theory > analytic number theory > L-function > Lefschetz zeta function

mathematical analysis > complex analysis > meromorphic function > L-function > Lefschetz zeta function

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Lefschetz zeta function

In mathematics, the Lefschetz zeta-function is a tool used in topological periodic and fixed point theory, and dynamical systems. Given a continuous map ${\\displaystyle f\\colon X\ o X}$ , the zeta-function is defined as the formal series

${\\displaystyle \\zeta _{f}(t)=\\exp \\left(\\sum _{n=1}^{\\infty }L(f^{n}){\ rac {t^{n}}{n}}\ ight),}$

where ${\\displaystyle L(f^{n})}$ is the Lefschetz number of the ${\\displaystyle n}$ -th iterate of ${\\displaystyle f}$ . This zeta-function is of note in topological periodic point theory because it is a single invariant containing information about all iterates of ${\\displaystyle f}$ .
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Lefschetz_zeta_function)

fonction zêta de Lefschetz

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