9 papers
Partial Breakdown of Integrability in Nearly Integrable Systems
Marian Gidea, Shoya Motonaga
We study the persistence of integrable structures in real-analytic nearly integrable systems under perturbations that may destroy some, but not all, of these structures. Specifical…
Explicit formulae and topological descriptions of action-minimizing sets of a full shift with an uncountable alphabet
Yuika Kajihara, Shoya Motonaga, Mao Shinoda
We completely solve ergodic optimization of a full shift with an uncountable alphabet , which is one of the most well-known examples of infinite dimensional dynamical system…
The Aubry set for the XY model and typicality of periodic optimization for 2-locally constant potentials
Yuika Kajihara, Shoya Motonaga, Mao Shinoda
We consider the Aubry set for the XY model, symbolic dynamics with the uncountable symbol , and study its action-optimizing properties. Moreover,…
Minimax aspects of optimizations in ergodic theory
Shoya Motonaga
We study optimization problems in ergodic theory from the view point of minimax problems. We give minimax characterizations of maximum ergodic averages involving time averages. Our…
Constrained Ergodic optimization for generic continuous functions
Shoya Motonaga, Mao Shinoda
One of the fundamental results of ergodic optimization asserts that for any dynamical system on a compact metric space with the specification property and for a generic continuous…
Properties of action-minimizing sets and weak KAM solutions via Mather's averaging functions
Shoya Motonaga
We study properties of action-minimizing invariant sets for Tonelli Lagrangian and Hamiltonian systems and weak KAM solutions to the Hamilton-Jacobi equation in terms of Mather's a…
Nonintegrability of Forced Nonlinear Oscillators
Shoya Motonaga, Kazuyuki Yagasaki
In recent papers by the authors (S.~Motonaga and K.~Yagasaki, Obstructions to integrability of nearly integrable dynamical systems near regular level sets, submitted for publicatio…
Obstructions to Integrability of Nearly Integrable Dynamical Systems near Regular Level Sets
Shoya Motonaga, Kazuyuki Yagasaki
We study the existence of real-analytic first integrals and real-analytic integrability for perturbations of integrable systems in the sense of Bogoyavlenskij including non-Hamilto…
Persistence of periodic and homoclinic orbits, first integrals and commutative vector fields in dynamical systems
Shoya Motonaga, Kazuyuki Yagasaki
We study persistence of periodic and homoclinic orbits, first integrals and commutative vector fields in dynamical systems depending on a small parameter and give s…