Equicontinuity And Periodic Orbits Of Triangular Maps

In the persent paper we mainly study equicontinuity and periodic orbits of a triangular map F of the square I~2.In Chapter One, we briefly introduce the historic background of dynamical system and some known results about equicontinuity and periodic orbits.In Chapter Two, we discuss equicontinuity of triangular maps.In this Chapter we show that the following five statements are equivalent for a triangular map F:(1) F is equicontinuous.(2) F4 is uniformly convergent.(3) F4 has property O.(4) G : (x, y) → ω((x, y), F~4) is continuous.(5) G : (x, y) → ω((x, y), F~4) is upper semi-continuous.In Chapter Three, we mainly study periodic orbits of triangular maps, we obtain the following results : (l)if F is a triangular map with R{F) = I~2then R(F) = Fix(F~4). (2)if a triangular map F has a cycle with over-rotation pair (p, q) and (p, q) ≥ (r, s), then F has a cycle with over-rotation pair (r, s).