Abstract: Lanzhou City is one of the most heavily air-polluted cities in China. In recent years，numerous researchers have lavished much attention on Lanzhou’s atmospheric environmental quality and air pollution. The dynamic analysis of pollution indexes，however，is rarely reported in the literature. In order to establish reasonable preventive countermeasures，it is important to understand the pollutant characteristics and the mechanisms of the pollution indexes’ temporal evolution. So，the objectives of this work were：（1） to prove the presence of chaos in air pollution index [（API] hereafter） time series；（2） to reflect the temporal evolution law of atmospheric pollutants and to identify dynamic variables to effectively interpret the changes of API time series in Lanzhou City. The time series of [API] during the past 10 years （from 2000 to 2010） in Lanzhou，northwest China，which is published on the website of Chinese Ministry of Environmental Protection （http://www.zhb.gov.cn/），were analyzed. In order to make full use of the abundant evolvement information contained in the API time series，the mutual information and CAO method were used to select the time delay and embedding dimension，and by reconstructing the multi-dimensional phase space，the characteristic quantities including the Lyapunov exponent，the correlation dimension and the Kolmogorov entropy，which could be taken as the chaotic features of the system，were calculated respectively. As a result，the correlation dimensions were fractioned，and the maximum Lyapunov exponent （λ₁＞0），which sufficiently shows that the time series of air pollution index over the past 10 years has fractal characteristics and chaotic characteristics. In the meanwhile，three or even four main dynamic variables （special valley basin topography，weather conditions，pollutant emissions and energy consumption structure） were discussed here that could effectively interpret the changes of air pollution index time series and their causes based on the calculated result of correlation dimension（D²=3.491 3）. These findings might provide a scientific basis for probing further into the regional complexity and evolution laws of the time series of air pollution index. At the same time，the identification of the chaotic characteristics also makes a base for non-linear forecast of the air pollution of Lanzhou City. And it has reference significance for improving the environment and promoting economy development of Lanzhou City.

Key words: air pollution index, time series, chaotic property, phase space reconstruction, correlation dimension, maximum Lyapunov exponent, Kolmogorov entropy, Lanzhou City