We construct non-uniform convergent lattices of pinched, negatively curved Hadamard spaces, in any dimension N > 2. These lattices are exotic, by which we mean that they have a maximal parabolic subgroup P < such that (P) = ().We also give examples of divergent, non-uniform exotic lattices in dimension N = 2. Finally, we consider a particular class of such exotic lattices, with infinite Bowen–Margulis measure and whose cusps have a particular asymptotic profile (satisfying a “heavy tail condition”), and we give precise estimates of their orbital function; namely, we show that their orbital function is lower exponential with asymptotic behaviour eR R1−L(R) , for a slowly varying function L.

Convergence and counting in infinite measure / Dal’bo, Françoise; Peigné, Marc; Picaud, Jean-Claude; Sambusetti, Andrea. - In: ANNALES DE L'INSTITUT FOURIER. - ISSN 0373-0956. - STAMPA. - 67:2(2017), pp. 483-520.

Convergence and counting in infinite measure

Sambusetti, Andrea
2017

Abstract

We construct non-uniform convergent lattices of pinched, negatively curved Hadamard spaces, in any dimension N > 2. These lattices are exotic, by which we mean that they have a maximal parabolic subgroup P < such that (P) = ().We also give examples of divergent, non-uniform exotic lattices in dimension N = 2. Finally, we consider a particular class of such exotic lattices, with infinite Bowen–Margulis measure and whose cusps have a particular asymptotic profile (satisfying a “heavy tail condition”), and we give precise estimates of their orbital function; namely, we show that their orbital function is lower exponential with asymptotic behaviour eR R1−L(R) , for a slowly varying function L.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1028764
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