CES Period Two At Critical

theorem proved Dynamics & Crises

Documentation

Lean 4 Proof

theorem ces_period_two_at_critical {J : ℕ} (hJ : 0 < J) {ρ : ℝ} (hρ : ρ < 1)
    {c : ℝ} (hc : 0 < c) :
    iterationMultiplier (cesCriticalStep J ρ c) (abs (cesEigenvaluePerp J ρ c)) = -1 :=
  iterMul_eq_neg_one_at_critical (cesEigenvaluePerp_abs_pos hJ hρ hc)

Dependency Graph

Location

thesis/CESProofs/Dynamics/DiscreteStability.lean:144

Module Section

Discrete-Time Stability of CES Tâtonnement (Edge of Stability)

In the same file

iterationMultiplier criticalStepSize abs_iterMul_lt_one_iff iterMul_eq_neg_one_at_critical one_lt_abs_iterMul_above_critical iterMul_in_unit_interval iterate_tendsto_zero iterate_norm_tendsto_top period_two_oscillation cesEigenvaluePerp_neg cesEigenvaluePerp_abs_pos cesCriticalStep cesCriticalStep_eq ces_stable_iff cesCriticalStep_increasing_in_rho cesCriticalStep_via_curvatureK eos_at_boundary eos_curvature_determines_step