Abstract. We present the first results of the surface photometry of a sample of Blue Compact Dwarf galaxies (hereafter BCDGs). The images were obtained at Pic du Midi (France) and Asiago (Italy). In this paper, we produce an atlas of isophotal maps and brightness distribution profiles for 23 objects in the Northern hemisphere. Short individual descriptions of the galaxies, and tables of photometric parameters are given.The main result is that a substantial fraction of objects are showing an r 1/4 brightness distribution, consistently with previous observations. The integral colors, luminosity-radius relations and "compactness" properties are briefly investigated. This sample is being extended with new observations, that will be reported in a future paper with a more complete discussion.

Abstract. We present the results of surface photometry on a new sample of Blue Compact Dwarf galaxies (BCDGs), in continuation to a previous paper (Doublier et al. 1997, hereafter Paper I). The 22 galaxies (plus two companions) discussed in the present paper have been selected in the Southern Hemisphere, from several lists. An atlas containing isophotal maps, surface brightnesses and B − R color profiles of the sample is given, together with the tables containing the photometric parameters.The results are consistent with those obtained in Paper I for objects selected from the Byurakan Surveys in the Northern hemisphere. Similarly, we find about one fourth of the BCDGs showing a dominant r 1/4 brightness distribution component, one fourth of the BCDG showing a dominant exponential surface brightness profile, and about half of them show composite brightness distributions. Integrated properties, colors, mean surface brightnesses and luminosity-radius relations are investigated and discussed for the objects presented in this paper and Paper I. We found that r 1/4 BCDGs tend to show a different behaviour compared to the exponential BCDGs, with respect to colors, compactness and luminosity-radius relations. We also include a brief study of the surroundings of the galaxies, where we find several candidate companions.Key words: galaxies: compact -galaxies: photometrygalaxies: starburst -galaxies: structure Send offprint requests to: V. Doublier Based on observations collected at the 1.54 m Danish Telscope at the European Southern observatory (La Silla, Chile).

We prove an analog of the Yomdin-Gromov lemma for p-adic definable sets and more broadly in a non-Archimedean definable context. This analog keeps track of piecewise approximation by Taylor polynomials, a nontrivial aspect in the totally disconnected case. We apply this result to bound the number of rational points of bounded height on the transcendental part of p-adic subanalytic sets, and to bound the dimension of the set of complex polynomials of bounded degree lying on an algebraic variety defined over C((t)), in analogy to results by Pila and Wilkie, and by Bombieri and Pila, respectively. Along the way we prove, for definable functions in a general context of non-Archimedean geometry, that local Lipschitz continuity implies piecewise global Lipschitz continuity.

We prove that a (globally) subanalytic function f : X ⊂ Q n p → Q p which is locally Lipschitz continuous with some constant C is piecewise (globally on each piece) Lipschitz continuous with possibly some other constant, where the pieces can be taken to be subanalytic. We also prove the analogous result for a subanalytic family of functions f y : X y ⊂ Q n p → Q p depending on p-adic parameters. The statements also hold in a semi-algebraic set-up and also in a finite field extension of Q p . These results are p-adic analogues of results of K. Kurdyka over the real numbers. To encompass the total disconnectedness of p-adic fields, we need to introduce new methods adapted to the p-adic situation.