Geometric estimates for the Schwarzian derivative

2017 ◽  
Vol 72 (3) ◽  
pp. 479-511 ◽  
Author(s):  
V N Dubinin
Keyword(s):  
Schwarzian Derivative ◽  
Geometric Estimates

GEOMETRIC ESTIMATES OF HERITABILITY IN BIOLOGICAL SHAPE

Evolution ◽  
2002 ◽  
Vol 56 (3) ◽  
pp. 563 ◽  
Author(s):  
Leandro R. Monteiro ◽  
José Alexandre F. Diniz-Filho ◽  
Sérgio F. dos Reis ◽  
Edilson D. Araújo
Keyword(s):  
Biological Shape ◽  
Geometric Estimates

UNIMODAL INTERVAL MAPS OBTAINED FROM THE MODIFIED CHUA EQUATIONS

1993 ◽  
Vol 03 (02) ◽  
pp. 323-332 ◽  
Author(s):  
MICHAŁ MISIUREWICZ
Keyword(s):  
Periodic Orbit ◽  
Critical Point ◽  
Real Line ◽  
Positive Measure ◽  
Schwarzian Derivative ◽  
Large Range ◽  
Unimodal Maps ◽  
Interval Maps ◽  
Central Piece ◽  
Piecewise Continuous

Following Brown [1992, 1993] we study maps of the real line into itself obtained from the modified Chua equations. We fix our attention on a one-parameter family of such maps, which seems to be typical. For a large range of parameters, invariant intervals exist. In such an invariant interval, the map is piecewise continuous, with most of pieces of continuity mapped in a monotone way onto the whole interval. However, on the central piece there is a critical point. This allows us to find sometimes a smaller invariant interval on which the map is unimodal. In such a way, we get one-parameter families of smooth unimodal maps, very similar to the well-known family of logistic maps x ↦ ax(1−x). We study more closely one of those and show that these maps have negative Schwarzian derivative. This implies the existence of at most one attracting periodic orbit. Moreover, there is a set of parameters of positive measure for which chaos occurs.

scholarly journals Dirichlet and VMOA domains via Schwarzian derivative

2009 ◽  
Vol 359 (2) ◽  
pp. 543-546 ◽  
Author(s):  
Fernando Pérez-González ◽  
Jouni Rättyä
Keyword(s):  
Schwarzian Derivative
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