Sentence examples for be a hyperbolic periodic from inspiring English sources

Let q be a hyperbolic periodic point of f.

Let p be a hyperbolic periodic point of f.

Let q ∈ H f (p) be a hyperbolic periodic point of f.

Proposition 2.6 Let p be a hyperbolic periodic point and let λ ∈ ( 0, 1 ) and L ≥ 1 be given.

Let f ∈ G 6 = G ″ ∩ G 5, and let q be a hyperbolic periodic point of f.

Let f ∈ G ′ = G 1, and let q be a hyperbolic periodic point in H f (p).

It is well known that if p is a hyperbolic periodic point of f with period k, then the sets W s ( p ) = { x ∈ M : f k n ( x ) → p  as  n → ∞ } and W u ( p ) = { x ∈ M : f − k n ( x ) → p  as  n → ∞ }. are C 1 -injectively immersed submanifolds of M. Lemma 2.4 Let p, q ∈ P ( f ) be hyperbolic saddles.

It is well known that if p is a hyperbolic periodic point of f with period k, then the sets W s ( p ) = { x ∈ M : f k n ( x ) → p  as  n → ∞ } and W u ( p ) = { x ∈ M : f − k n ( x ) → p  as  n → ∞ }. are C 1 -injectively immersed submanifolds of M. Denote by C f ( p ) the chain component of f containing p. If p is a sink or source periodic point, then C f ( p ) is a periodic orbit itself.

It is well known that if p is a hyperbolic periodic point of f with a period k, then the sets W s ( p ) = { x ∈ M : f k n ( x ) → p  as  n → ∞ } and  W u ( p ) = { x ∈ M : f − k n ( x ) → p  as  n → ∞ }. are C 1 -injectively immersed submanifolds of M. Let p, q ∈ P ( f ) be saddles.

(b) C f (p) = H f (p), where p is a hyperbolic periodic point ([5]).

Note that if p is a hyperbolic periodic point of f then p does not have the δ-weak eigenvalue.