Why does the fault exist in the crust ? Why is rock deformed
rheologically by stress ? Why do the deformation-fracturing phenomenon
have a variety of kinds of duality (e.g . Hodge duality) and symmetry
properties (e.g., Fractal) ? I study the deformation-fracture theory of
the crust including a fault defect field to clear the origin of the
duality and symmetry in deformation-fracturing processes
K. Yamasaki and T. Yajima, 2017, ”KCC analysis of the nornal form of typical bifurcations
in one-dimensional dynamical system: geometrical invariants of saddle-node, transcritical, and pitchfork bifurcations”, Int. J. Bifurcation and Chaos, 27, 1750145 (14 pages).
K. Yamasaki and T. Yajima, 2016, “Differential geometric structure of non-equilibrium dynamics in competition and predation:
Finsler geometry and KCC theory”, J. Dynamical Systems & Geometric Theor., 14, 137-153.
N. Nakamura and K. Yamasaki, 2016, “Feynman’s Proof and Non-Elastic Displacement Fields:
Relationship Between Magnetic Field and Defects Field”, Int. J. Theoretical Physics, 12, 5186-5192.
T. Yajima and K. Yamasaki, 2016,“Jacobi stability for dynamical systems of two-dimensional second-order differential equations
and application to overhead crane system”, Int. J. Geometrical Methods in Modern Phys., 13, 1650045.