The blood glucose and plasma insulin responses to some simple carbohydrates (glucose, fructose, lactose) and some complex ones (apples, potatoes, bread, rice, carrots and honey) were studied in 32 Type 2 (non-insulin-dependent) diabetic patients. Blood glucose and plasma insulin were measured at zero time and then at 15, 30, 60, 90 and 120 min after ingestion of 25 g glucose, fructose or lactose, or 30 g honey, 50 g white bread, 125 g white rice or potatoes, 150 g apples or 260 g carrots. Maximum blood glucose and plasma insulin responses were recorded 60 min after ingestion of each test meal. At this time the increases in blood glucose and in plasma insulin were significantly higher after the more refined carbohydrates (glucose, fructose and lactose) than after the more complex ones (apples, potatoes, rice, carrots and honey, -p less than 0.01). Counting the blood glucose increase after glucose as 100%, the corresponding increases in glycaemia for other carbohydrates were: fructose, 81.3%; lactose, 68.6%; apples, 46.9%; potatoes, 41.4%; bread, 36.3%; rice, 33.8%; honey, 32.4% and carrots, 16.1%.

The moduli space M d of degree d ≥ 2 rational maps can naturally be endowed with a measure µ bif detecting maximal bifurcations, called the bifurcation measure. We prove that the support of the bifurcation measure µ bif has positive Lebesgue measure. To do so, we establish a general sufficient condition for the conjugacy class of a rational map to belong to the support of µ bif and we exhibit a large set of Collet-Eckmann rational maps which satisfy that condition. As a consequence, we get a set of Collet-Eckmann rational maps of positive Lebesgue measure which are approximated by hyperbolic rational maps.

We prove that the Collet-Eckmann condition for recurrent critical orbits inside the Julia set of a rational map with no parabolic periodic orbits implies uniform hyperbolicity on periodic orbits. IntroductionLet f be a rational map, J its Julia set and Crit the set of critical points. We know that J is hyperbolic if and only if the closure of the postcritical set O(Crit) is disjoint from J . If we let some critical points with finite orbit be in the Julia set it becomes sub-hyperbolic. The next step is to allow infinite critical orbits in J as long as they do not accumulate on any critical point and rule out parabolic periodic orbits (the Misiurewicz condition). Semi-hyperbolicity is even weaker, it requires that critical orbits should not be recurrent, in the absence of parabolic periodic points. Under this assumption Carleson et al show that the Fatou components are John domains for polynomials (see [4]). Every John domain is a Hölder domain. The property that all Fatou components are Hölder is equivalent to uniform hyperbolicity on periodic orbits (see [5] and [10]). Another advance in this direction was made by Graczyk and Smirnov (initiated in [5] and developed in [6]) by allowing recurrent critical points in the Julia set. If all the critical points in J are Collet-Eckmann (CE) then all Fatou components are Hölder. We propose a new sufficient condition for uniform hyperbolicity on periodic orbits (UHP). It allows for both non-recurrent and CE critical points in the Julia set, in the absence of parabolic periodic orbits.It is known that a semi-hyperbolic rational map is not necessarily CE and vice versa, see [10, §6.1.1] and [7, §1.2]. Therefore, UHP does not imply CE nor semi-hyperbolicity. However, for unicritical polynomials, the CE condition is equivalent to UHP (see [5] and [9]). To our knowledge there is no counterexample to the converse of our main theorem.A related problem is the invariance of such regularity or growth conditions under topological conjugacy. Semi-hyperbolicity (by definition) and UHP (see [10]) are

We show that the Fatou components of a semi-hyperbolic rational map are John domains. The converse does not hold. This compares to a famous result of Carleson, Jones and Yoccoz for polynomials, in which case the two conditions are equivalent.We show that a connected Julia set is locally connected for a large class of nonuniformly hyperbolic rational maps. This class is more general than semi-hyperbolicity and includes Collet-Eckmann maps, topological Collet-Eckmann maps and maps satisfying a summability condition (as considered by Graczyk and Smirnov).