On the Appearance of Mixed Dynamics as a Result of Collision of Strange Attractors and Repellers in Reversible Systems

Chaplygin sleigh in the quadratic potential field

“…At once the attractor and the repeller instantly increase in size. Such behaviour has been found in the nonholonomic model of the Suslov top and in the dynamics of vortices [25,26].…”

“…called mixed [21][22][23][24][25][26], which is distinguished from conservative and pure dissipative. The trajectories of attractors and repellers become intertwined in such a complex manner, that they cannot be separated from each other.…”

“…The trajectories of attractors and repellers become intertwined in such a complex manner, that they cannot be separated from each other. A particular scenario of mixed dynamics emergence was proposed recently for two-dimensional reversible diffeomorphisms [25,26]: invariant manifolds of the saddle points belonging to chaotic attractor and to repeller intersect each other, accompanied by a collision of the attractor with the repeller. At once the attractor and the repeller instantly increase in size.…”

Reversible perturbations of conservative Hénon-like maps

“…The second side (to prove) is much delicate than the first one, it requires involving various theoretical aspects of mixed dynamics such as criteria for the existence of absolute Newhouse regions [GST97, LS04, Tur10, GGS20] and the structure of bifurcation scenarios leading to the appearance of mixed dynamics, see e.g. [GGKT17,Kaz19,Kaz20]. In the present paper we apply both these approaches when studying local and global bifurcations.…”

“…Note that the reversible core can be vast and occupy a large part of the phase space and, thus, mixed dynamics becomes an observable phenomenon in applications, see e.g [6,7,8,13,18,19]…”