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math.DS2021
Unfolding globally resonant homoclinic tangencies
Sishu Shankar Muni, Robert I. McLachlan, David J. W. Simpson
Global resonance is a mechanism by which a homoclinic tangency of a smooth map can have infinitely many asymptotically stable, single-round periodic solutions. To understand the bi…
math.DS2020
Homoclinic tangencies with infinitely many asymptotically stable single-round periodic solutions
S. S. Muni, R. I. McLachlan, D. J. W. Simpson
We consider a homoclinic orbit to a saddle fixed point of an arbitrary map on and study the phenomenon that has an infinite family of asymptotical…