Discontinuous Dynamical Systems on Time-varying Domains is the first monograph focusing on this topic. While in the classic theory of dynamical systems the focus is on dynamical systems on time-invariant domains， this book presents discontinuous dynamical systems on time-varying domains where the corresponding switchability of a flow to the time-varying boundary in discontinuous dynamical systems is discussed. From such a theory， principles of dynamical system interactions without any physical connections are presented. Several discontinuous systems on time-varying domains are analyzed in detail to show how to apply the theory to practical problems. The book can serve as a reference book for researchers， advanced undergraduate and graduate students in mathematics， physics and mechanics.

Front Matter
1 Introduction
  1.1 Discontinuous systems
  1.2 Book layout
  References
2 Flow Switchability
  2.1 Discontinuous dynamic systems
  2.2 G-functions
  2.3 Passable flows
  2.4 Non-passable flows
  2.5 Tangential flows
  2.6 Switching bifurcations
  References
3 Transversality and Sliding Phenomena
  3.1 A controlled system
  3.2 Transversality conditions
  3.3 Mappings and predictions
  3.4 Periodic and chaoticmotions
  References
4 A Frictional Oscillator on Time-varying Belt
  4.1 Mechanicalmodel
  4.2 Analytical conditions
   4.2.1 Equations ofmotion
   4.2.2 Passable flows to boundary
   4.2.3 Sliding flows on boundary
   4.2.4 Grazing flows to boundary
  4.3 Generic mappings and force product criteria
   4.3.1 Genericmappings
   4.3.2 Sliding flows and fragmentation
   4.3.3 Grazing flows
  4.4 Periodicmotions
   4.4.1 Mapping structures
   4.4.2 Illustrations
  4.5 Numerical simulations
  References
5 Two Oscillators with Impacts and Stick
  5.1 Physical problem
   5.1.1 Introduction to problem
   5.1.2 Equations ofmotion
  5.2 Domains and vector fields
   5.2.1 Absolutemotion description
   5.2.2 Relativemotion description
  5.3 Mechanismof stick and grazing
   5.3.1 Analytical conditions
   5.3.2 Physical interpretation
  5.4 Mapping structures andmotions
   5.4.1 Switching sets and basicmappings
   5.4.2 Mapping equations
   5.4.3 Mapping structures
   5.4.4 Bifurcation scenario
  5.5 Periodicmotion prediction
   5.5.1 Approach
   5.5.2 Impacting chatter
   5.5.3 Impacting chatterwith stick
   5.5.4 Parametermaps
  5.6 Numerical illustrations
   5.6.1 Impacting chatter
   5.6.2 Impacting chatterwith stick
   5.6.3 Further illustrations
  References
6 Dynamical Systems with Frictions
  6.1 Problemstatement
  6.2 Switching and stick motions
   6.2.1 Equations ofmotion
   6.2.2 Analytical conditions
  6.3 Periodicmotions
   6.3.1 Switching planes andmappings
   6.3.2 Mapping structures andmotions
   6.3.3 Bifurcation scenario
  6.4 Numerical illustrations
   6.4.1 Periodic motion without stick
   6.4.2 Periodicmotionwith stick
   6.4.3 Periodicmotionwith stick only
  References
7 Principles for System Interactions
  7.1 Two dynamical systems
   7.1.1 Dynamical systems with interactions
   7.1.2 Discontinuous description
   7.1.3 Resultant dynamical systems
  7.2 Fundamental interactions
  7.3 Interactions with singularity
  7.4 Interactions with corner singularity
  References
Appendix
  A.1 Basic solution
  A.2 Stability and bifurcation
Index
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非线性物理科学系列NPS