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Infinite invariant densities due to intermittency in a nonlinear oscillator

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Meyer,  Philipp
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Kantz,  Holger
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Citation

Meyer, P., & Kantz, H. (2017). Infinite invariant densities due to intermittency in a nonlinear oscillator. Physical Review E, 96(2): 022217. doi:10.1103/PhysRevE.96.022217.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002E-27FC-6
Abstract
Dynamical intermittency is known to generate anomalous statistical behavior of dynamical systems, a prominent example being the Pomeau-Manneville map. We present a nonlinear oscillator, i.e., a physical model in continuous time, whose properties in terms of weak ergodity breaking and aging have a one-to-one correspondence to the properties of the Pomeau-Manneville map. So for both systems in a wide range of parameters no physical invariant density exists. We show how this regime can be characterized quantitatively using the techniques of infinite invariant densities and the Thaler-Dynkin limit theorem. We see how expectation values exhibit aging in terms of scaling in time.