Let ({x_{i}}_{i=0}^{N}) be an orbit of a chaotic map and consider the coverage of its attractor by hypercubes of edge length ℓ.
An orbit of a multivalued map, the collection of nonempty subsets of, at is a sequence.
A key feature of an orbit of a degree-one circle map is its "rotation number".
Let X = ( f 1, f 2, …, f n, … ) (1). be an infinite bounded numerical sequence-this can be some time series, discrete-time signal, experimental data (long enough), or an orbit of iterates of some map.
Therefore an orbit of length N of a map f(x) has threshold (s_{text {th}}triangleq L/N), where L is the length of the curve and is obtained from the well-known formula from calculus L=int^{1}_{-1}sqrt{1+[f'(x)]^{2}}dx.
An orbit O x0) of a multi-valued map T at a point x0 is a sequence {x n : x n ∈ Txn-1, n = 1, 2,...}.
This can be some time series, experimental data, or an orbit of iterates of some one-dimensional map.
Therefore, the subcritical flip bifurcation occurs at point ((y^, V_{L}^{3*})), and there exists a constant (epsilon>0) such that the Poincaré map has an orbit of period two which is unstable for (V_{L}^{1*}< V_{L}^{3*}-epsilon< V_{L}< V_{L}^{3*}).
An orbit of at is a sequence.
Let be a complete quasimetric space and let be a generalized -contractive map, then there exists an orbit of at, such that the sequence of nonnegative numbers is decreasing to zero and is a Cauchy sequence.
Then from Theorem 4.1 we know that if we let γ < 0.115 … slightly an attractive 2-periodic orbit of map F emerges and if let γ ≥ 0.115 … the 2-periodic orbit does not exist, but a stable equilibrium point occurs.
