Rigidity and sensitivity on uniform spaces

Topological chain and shadowing properties of dynamical systems on uniform spaces

“…Das et al [6] generalized the usual definitions in metric spaces of expansivity, shadowing, and chain recurrence for homeomorphisms to topological spaces. We [14] introduced the topological concepts of weak uniformity, uniform rigidity, and multi-sensitivity and obtained some equivalent characterizations of uniform rigidity. Then, we [15] proved that a point transitive dynamical system is either sensitive or almost equicontinuous.…”

Shifts, rotations and distributional chaos

“…The notion of Li-Yorke sensitivity was firstly introduced by Akin and Kolyada [1] in 2003. More recent results on chaos can be found in [2,3,7,17,18,[20][21][22][23][24][25][26][27][28][29][30][31].…”

Distributional Chaoticity of C0-Semigroup on a Frechet Space

“…Chaotic properties of dynamical systems have been ardently studied since the term chaos (namely, Li-Yorke chaos) was defined in 1975 by Li and Yorke [1]. To describe unpredictability in the evolution of dynamical systems, many properties related to chaos have been discussed (for example, References [2][3][4][5][6][7][8][9][10][11][12][13], where References [4][5][6][7] are some of our works done in recent years). In 1994, Schweizer and Smital in Reference [8] introduced a popular concept named distributional chaos for interval maps, by considering the dynamics of pairs with some statistical properties.…”