{'fraction_non_alphanumeric': 0.009380863039399626, 'fraction_numerical': 0.0, 'mean_word_length': 4.868131868131868, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A dynamical study of the Friedmann equations

Cosmology is an attractive subject for students but it is usually difficult if general relativity is not understood. In this article, we first recall the Newtonian derivation of the Friedmann equations which govern the dynamics of our universe and discuss the validity of such a derivation. We then study the equations of evolution of the universe in terms of a dynamical system. This sums up the different behaviours of our universe and enables us to address some cosmological problems.