Abstract
This paper is devoted to studying the multiple recurrent property of topologically mildly mixing systems along generalized polynomials. We show that if a minimal system is topologically mildly mixing, then it is mild mixing of higher orders along generalized polynomials. Precisely, suppose that (X,T) is a topologically mildly mixing minimal system, d∈N, p1,…,pd are integer-valued generalized polynomials with (p1,…,pd) non-degenerate. Then for all non-empty open subsets U,V1,…,Vd of X,{n∈Z:U∩T−p1(n)V1∩…∩T−pd(n)Vd≠∅} is an IP⁎-set.
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